Questions on Geometry: Triangles answered by real tutors!

Tutors Answer Your Questions about Triangles (FREE)

Question 1210652: Precalculus
Michael Sullivan
Section 1.1
Q. 69
When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an ERROR TRIANGLE. If this error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side.
Let A, B, and C = three lines in quadrant I on the xy-plane. Plot all three lines in quadrant I on the xy-plane. Connect the three lines through the given three points.
A meets B at the point (2.7, 1.7).
A meets C at the point (2.6, 1.5).
B meets C at the point (1.4, 1.3).
(I) Find an estimate for the desired intersection point.
(II) Find the length of the median for the midpoint found in part I.

Click here to see answer by ikleyn(53956)

Question 1210649: Precalculus
Michael Sullivan
Section 1.1
Q. 56
An equilateral triangle is one in which all three sides are of equal length.
If two vertices of an equilateral triangle are (0,4) and (0,0), find the third vertex. How many of these triangles are possible?
Click here to see answer by ikleyn(53956)

Question 1210647: Precalculus
Section 1.1
Q. 32
A. Plot each point on the xy-plane and form triangle ABC.
B. Show that triangle ABC is a right triangle.
C. Find its area.
Points: A= (-2, 5), B = (12, 3), C = (10, -11)

For Part A, I don't know how to upload photos to this site. Does anyone know?
For Part B, I need to use the distance formula for points on the xy-plane three times. In other words, I must find d(A,B), d(B,C) and d(A,C). Is this correct?
For Part C, I need to use the answer to Parts A and B to find the area of triangle ABC. Is this right?

Click here to see answer by ikleyn(53956)

Question 945295: The base of an isosceles triangle is 3 more than 2 times the length of the legs and the perimeter is 23. What is the length of the base?

Click here to see answer by josgarithmetic(39839)

Question 271612: the area of a triangle is 20 square centimeters. what are the possible whole-number dimensions for the base and height of the triangle?
Click here to see answer by ikleyn(53956)

Question 264317: I have an isoceles with an angle supplementary to angle 3 equaling 116 degrees find angles 1 and 2.
Click here to see answer by josgarithmetic(39839)

Question 264317: I have an isoceles with an angle supplementary to angle 3 equaling 116 degrees find angles 1 and 2.
Click here to see answer by ikleyn(53956)

Question 263303: A lawn is in the shape of a trapezoid with a height of 60 ft and bases of 70ft and 130 ft. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 4000 square feet.
Click here to see answer by ikleyn(53956)

Question 1210553: The three angles 𝐴, 𝐵, and 𝐶 of the figure shown below are given by (7⁢𝑥−40)∘, (5⁢𝑥)∘, and (8⁢𝑥)∘, respectively. What is the value of 𝑥 ?
Click here to see answer by greenestamps(13370)

Question 447784: Is a triangle with sides9 9 units, 16units and 25 units a right triangle
Click here to see answer by ikleyn(53956)

Question 732184: A triangle has two sides that measure 4.56 cm and 8.65 cm. Which could be the measure of the third side?
A. 3.95 cm
B. 10.31 cm
C. 13.21 cm
D. 20.25 cm
Click here to see answer by ikleyn(53956)

Question 733048: What is the measure of each base angle of an isosceles triangle if its vertex angle measures 24 degrees and its two congruent sides measure 11 units?
Click here to see answer by ikleyn(53956)

Question 744585: given a triangle with a leg 13 km and hypotenuse 23 km find the missing side
Click here to see answer by ikleyn(53956)

Question 674343: how do I find the area of an iscoseles triangle when I've only been given the measurements of two sides using the sine rule: 1/2(ab)sinC
Click here to see answer by ikleyn(53956)

Question 476956: I'm trying to figure out how to find the perimeter to an isosceles triangle where I am only given one side which is 14, and the only other information is that the other two sides are congruent.
Click here to see answer by ikleyn(53956)

Question 478143: how do you find the largest angle of a triangle with sides 4cm, 7cm and 9cm?
Click here to see answer by ikleyn(53956)

Question 480043: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Click here to see answer by greenestamps(13370)

Question 480043: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Click here to see answer by Edwin McCravy(20086)

Question 480043: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Click here to see answer by ikleyn(53956)

Question 1157698: In ΔRST, angle R = 140° and side s = (3/4)r. Find the measures of angles S and T.
Click here to see answer by ikleyn(53956)

Question 1164146: Two sides of a triangle are AB=34cm and AC=25cm and their included angle measure 62°. Question is, Find the distance of the orthocenter to side AB.
Click here to see answer by ikleyn(53956)

Question 1178105: The longest side of a triangular building lot has length 190 meters and the next longer side is 180 meters (the shortest length is unknown). The angle between the longer sides measures 54º. Using the median to the longest side (the segment joining the midpoint of the side to the opposite vertex) the lot is divided into two lots with equal area. Find the length of the median to the nearest tenth of a meter.
Click here to see answer by ikleyn(53956)

Question 1210262: Let ABC be a triangle with side lengths AB = 5, BC = 6, and AC = 9. What is the area of the triangle with side lengths \tan A$, \tan B, and \tan C?

Click here to see answer by ikleyn(53956)

Question 1210260: Find the area of the triangle with side lengths 4, 5, and 8.

Click here to see answer by ikleyn(53956)

Question 1210242: In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BD=12, AE=8, and BF=3+AE. Find AB.

Click here to see answer by ikleyn(53956)

Question 1210243: In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AE = 11, BE = 9, and AD = 6\sqrt{2}, what is AF?

Click here to see answer by CPhill(2264)

Question 1210193: Triangle ABC has AB = 6. Let D lie on BC such that \overline{AD} bisects \angle BAC. If BD = 3 and CD = 5, what is CD?
Click here to see answer by greenestamps(13370)

Question 1210193: Triangle ABC has AB = 6. Let D lie on BC such that \overline{AD} bisects \angle BAC. If BD = 3 and CD = 5, what is CD?
Click here to see answer by ikleyn(53956)

Question 1210193: Triangle ABC has AB = 6. Let D lie on BC such that \overline{AD} bisects \angle BAC. If BD = 3 and CD = 5, what is CD?
Click here to see answer by CPhill(2264)

Question 1210190: Chris places an orange cone at his current location. Then, he faces west, walks 40 meters, turns 30^{\circ} to his right, and walks 20 meters. How far is Chris from the cone, in meters? Round your answer to the nearest whole number.
(You will need to use a calculator.)

Click here to see answer by CPhill(2264)

Question 1210147: In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.
Click here to see answer by ikleyn(53956)

Question 1210147: In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.
Click here to see answer by CPhill(2264)

Question 1210137: The left column contains pairs of triangles with different side-length and angle-measure congruences marked. Match each diagram in the left column with a congruence/similarity criterion in the right column that justifies why the two triangles are congruent/similar. Duplicates are NOT permitted. Note: to undo a connection, click the link itself, not one of the boxes in the columns.
Click here to see answer by CPhill(2264)

Question 1210138: The left column contains pairs of triangles with different side-length and angle-measure congruences marked. Match each diagram in the left column with a congruence/similarity criterion in the right column that justifies why the two triangles are congruent/similar. [b]Duplicate answers ARE permitted[/b]. (Note: to undo a connection, click the link itself, not one of the boxes in the columns.)
Click here to see answer by CPhill(2264)

Question 1210139: In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AB = 11, AC = 12, and AD = 6, what is AF?

Click here to see answer by CPhill(2264)

Question 1210136: In the diagram below, we know \tan \theta = \frac{3}{4}. Find the area of the triangle.

The triangle is right, and the hypotenuse is 80.
Click here to see answer by math_tutor2020(3838)

Question 1169820: Give a formal proof of the following theorem
1. A quadrilateral with one pair of opposite sides equal and parallel is a parallelogram. (Construct a diagonal).
2. If both pairs of opposite sides of a quadrilateral are equal, the quadrilateral is a parallelogram. (Construct a diagonal).
3. The diagonals of a rhombus, (i) bisect each other at right angles, (ii) bisect the angles of the rhombus.
Click here to see answer by CPhill(2264)

Question 1169822: Please help me to solve this.. DEF is a triangle with angle EDF=2x°. Line DE and line DF are produced to G and H respectively so that side EF=side EG=side FH. Line EH and line FG intersect at K. Show that angle EKG=90-x°. Thank you
Click here to see answer by CPhill(2264)

Question 1168324: In a basketball league of x teams of which every team plays every other twice, the total number of games played is x²-x
a. How many teams are there in a league the plays a total of 72 games?
b. If there were 6 teams in the league, how many in all would be played?
Click here to see answer by ikleyn(53956)

Question 1174508: Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, d represents the distance from a star to the Sun. Using a technique called “stellar parallax,” astronomers determined \large \theta is 0.00001389 degrees. How far away is the star from the Sun in astronomical units? Show your reasoning.
Click here to see answer by CPhill(2264)

Question 1174947: Show that if ∆A'B'C' is the image of ∆ABC under a dilation with center O and scale
factor k, then
∆A'B'C' ∆ABC = k
2
Click here to see answer by CPhill(2264)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735