Questions on Geometry: Triangles answered by real tutors!

Tutors Answer Your Questions about Triangles (FREE)

Question 1190312: Find the area, in square units, of an isosceles triangle whose sides have lengths 29, 29, and 42 cm without using Heron's formula
Click here to see answer by ikleyn(52772)

Question 1190315: A triangle has sides 33, 56, and 65. What is the length of the altitude to the longest side using similar triangles only?
Click here to see answer by ikleyn(52772)

Question 1190322: If s is the semi-perimeter of triangle ABC and r is the radius of its incircle, what is the area of triangle ABC in terms of r and s?
Click here to see answer by ikleyn(52772)

Question 1190327: A triangle with sides of length 36 cm, 77 cm, and 85 cm are inscribed in a circle. Inside the triangle a second circle is inscribed. What is the area in square centimetres, between the two circles?
Click here to see answer by ikleyn(52772)

Question 1190328: A 5-12-13 triangle is inscribed in a circle, which is inscribed in a larger 5-12-13 triangle. What is the ratio of the area of the smaller triangle to the area of the larger triangle?
Click here to see answer by ikleyn(52772)

Question 1190333: From the top of a lighthouse 60m high, a boat with an angle of depression of 37° If the boat travels linearly 35m towards the tower. What is the new angle of
elevation?
Click here to see answer by Alan3354(69443)

Question 1190330: A square is inscribed in a circle, which in turn is inscribed in an equilateral triangle. If the area of the square is 16, what is the area of the region inside the triangle but outside the circle?
Click here to see answer by greenestamps(13198)

Question 1190375: A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counterclockwise.
What are the coordinates of the child after 45 seconds?
Click here to see answer by math_tutor2020(3816)

Question 1190383: A five-foot sophomore at D-E casts an eight-foot shadow. How high is the Sun in the sky? This question is not asking for a distance, by the way.
I found the hypotenuse of the triangle and I'm not sure where to proceed. I have also done tan of 5/8 which gets me 0.625, but I still have no idea for how to do this.
Click here to see answer by math_tutor2020(3816)

Question 1190453: A 20-foot ladder is leaned against a wall, with the top of the ladder at the height of 15 ft. What is the angle of inclination of the ladder?

Click here to see answer by Theo(13342)

Question 1190603: The large equilateral triangle has sides of units. The midpoints of the large triangle are
joined to form the second triangle. The midpoints of the second triangle are joined to form the
third triangle. The process of joining midpoints to form new triangles continues indefinitely
State the height of all 3 in terms of p
Determine the areas of all 3 in terms of p

Click here to see answer by greenestamps(13198)

Question 1191360: Write the following equation in polar form: x^2+y^2+12y=0
Click here to see answer by MathLover1(20849)

Question 1191359: Transform the following equation to a cartesian equation: r=sec(theta)tan^2(theta)
Click here to see answer by MathLover1(20849)

Question 1191368: Find the value of x in each pair of similar figures.
1st picture is a triangle with Q,O,P at each corner. Between Q and O is 5mi, Between Q and P has 6mi.
2nd picture is also a triangle with R,S,T one letter at each corner. Between R and T is xmi, Between T and S has 30mi.
Im trying to help my son with his homework but we dont know how to solve this
Click here to see answer by ikleyn(52772)

Question 1191537: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

Click here to see answer by josgarithmetic(39615)

Question 1191537: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

Click here to see answer by ikleyn(52772)

Question 1191537: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

Click here to see answer by math_tutor2020(3816)

Question 1191597: A right isosceles triangle has equal sides of d cm and sqrt(12+d) cm. Find the length of the hypotenuse in simplest radical form.
Click here to see answer by greenestamps(13198)

Question 1191777: What is the ratio of the longer leg to the hypotenuse in a 30-60-90 triangle?
What is the ratio of a leg to the hypotenuse in a 45-45-90 triangle?
Click here to see answer by josgarithmetic(39615)

Question 1191785: If the triangle FGH is similar to the triangle RST, which side is proportional to side FH?
Click here to see answer by ikleyn(52772)

Question 1191818: The length of the longest side is the integer given. What value(s) of x make the triangle? x-4 , x+7, 45 ; Acute triangle
Click here to see answer by greenestamps(13198)

Question 1191939: 30. A hill slopes at an angle of 12^ 28^ prime with the horizontal . From the base of the hill , the angle of inclination of a 459.0 ft tower at the top of the hill is 35^ 9^ prime . How much rope would be required to reach from the top of the tower to the bottom of the hill?
Click here to see answer by Alan3354(69443)

Question 1192556: How do I find x in a triangle?
Click here to see answer by MathLover1(20849)

Question 1192734: PROBLEM SOLVING. Analyze. Solve. Answer.
Draw diagrams wherever necessary. Round off your final answers up to 2 decimal places.
1.A 4.5-meter ladder leans against a building. If the top of the ladder is 3.75 meters above the ground, what is the angle made by the ladder with the ground?
2.Lisa stands at a distance of 60 m away from the base of a certain statue, making a 23° angle of elevation to the top. What is the height of the statue?
3.At a certain time of the day, the angle of elevation of the sun is 52°, what is the length of the shadow on the level ground of a man who is 1.67 m tall?
4.A pole was put up on a lake and stands 13 meters from the surface of the lake. From the top of the pole, the angle of depression of a small bunch of fishes on the other side of the lake is 32°. What is the distance from the base of the pole to the location of the fishes?
5.Sara and Junya made a string telephone and tested if it works. Sara stood at the top of a tower while Junya stayed at the ground level. From Sara’s viewpoint, the angle of depression of Junya is 64° with the horizontal. Junya is 10.5 m from the base of the tower. How long is the string of their improvised telephone?
Click here to see answer by ikleyn(52772)

Question 1192921: 15+x
Click here to see answer by MathLover1(20849)

Question 1192922: x+11=
x-6+4=
(5x)°+(2x+3)°=
4x+ 2x+18=
(2x)°+ (20)°
15+x
Click here to see answer by ikleyn(52772)

Question 1193470: You’re given three angle measurements of 30°, 70°, and 80°. How many triangles can you construct using these measurements?

Click here to see answer by ikleyn(52772)

Question 1193763: the perimeter of a two-sided triangle is 70cm. The lateral rib is 5cm longer than the base. Find the surface of the square that is built on one of the side ribs
Click here to see answer by ikleyn(52772)

Question 1193947: if an angle θ is a principal angle that lies in the quadrant 3 such that 0 degrees ≤ θ ≤ 360 degrees, determine the exact value of x, y and r for tan θ= 2/3 and draw the diagram

I got for x=3 y=2 and r= square root of 13 not sure how to draw it though
Thanks
Click here to see answer by ikleyn(52772)

Question 1194154: Point p(-5,-8) is on the terminal arm of the angle ,θ, in standard position. Determine all the values of θ for -540 degrees ≤ θ ≤ 270 degrees

I found the principal angle of 238 degrees and the related acute angle of 58 degrees. Then I am stuck from there for the other values.

Click here to see answer by ikleyn(52772)

Question 1194385: A right triangle has a hypotenuse of 9 yards. If one of the angles is 3 degrees, what is the area of this triangle? Explain your work.

Click here to see answer by math_tutor2020(3816)

Question 1194384: An 8 foot ladder is leaning against a building. The angle the ladder makes with the wall is 11 degrees. How far up the building does the ladder reach? Show your work.
Click here to see answer by ikleyn(52772)

Question 1194476: Two sides of a triangle are 7 and 13. What are all possible lengths of the third side, x?
Click here to see answer by josgarithmetic(39615)

Question 1194529: In triangle ABC, with right angle B, side AB is 18 units long and side AC is 23 units long. What is the length of side BC, to the nearest unit?
5 units
14 units
29 units
41 units
Click here to see answer by MathLover1(20849)

Question 1194776: Richard, Anton, and Donald are standing at three comers of a triangle in the middle of a park. Donald is 54 m from Anton, and Richard is 74 m from Donald. The angle at the of the triangle where Richard is standing is 34 degrees a) Sketch possible diagrams for this situation. b) Calculate the possible distance(2) from Richard to Anton.
Thank you
Click here to see answer by josgarithmetic(39615)

Question 1194922: the tangent and normal to the curve y=4*sqrt(x+2) at the point P(7,12) cut the x-axis at M and N respectively. Calculate the area of the triangle PMN
Click here to see answer by math_helper(2461)

Question 1194972: In the diagram below, XY = 4, YZ = 6. What is the length of YV?

Click here to see answer by MathLover1(20849)

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