Questions on Geometry: Geometric formulas answered by real tutors!

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Question 1193806: Given: △XYZ with XY ≅ XZ ≅ YZ ZW ⊥ XY with W on XY YZ = 8
Find: ZW
Find the measures of the following angles in degrees.
m∠WYZ =
°
m∠YWZ =
°
m∠YZW =
°
Find WY.
WY =
Find The simplest radical form of simplest radical form ZW

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Question 1193780: Given:
△XYZ with XY ≅ XZ ≅ YZ ZW ⊥ XY with W on XY YZ = 8
Find: ZW
Find the measures of the following angles in degrees.
m∠WYZ =
°
m∠YWZ =
°
m∠YZW =
°
Find WY.
WY =
Find ZW. Give your answer in both simplest radical form and as an approximation correct to two decimal places.
simplest radical form ZW =

approximation ZW =

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Question 1193620: Given: right △RST with
RT = 8radical 2
and m∠
STV = 150°
Find: RS and ST
△R S T has vertices R on the left, S on top, and T on the right. ∠S is a right angle. A point labeled V lies to the right of T. The horizontal line segment that connects R and T continues to the right and ends at V.
simplest radical form RS =

approximation RS =
simplest radical form ST =

approximation ST =

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Question 1193620: Given: right △RST with
RT = 8radical 2
and m∠
STV = 150°
Find: RS and ST
△R S T has vertices R on the left, S on top, and T on the right. ∠S is a right angle. A point labeled V lies to the right of T. The horizontal line segment that connects R and T continues to the right and ends at V.
simplest radical form RS =

approximation RS =
simplest radical form ST =

approximation ST =

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Question 1193683: Consider the following.
Given: △XYZ with XY ≅ XZ ≅ YZ ZW ⊥ XY with W on XY
YZ = 8
Find:ZW
m∠WYZ =
°
m∠YWZ =
°
m∠YZW =
°
Find WY.
WY =
Find ZW. Give your answer in both simplest radical form and as an approximation correct to two decimal places.
simplest radical form ZW =

approximation ZW =

Click here to see answer by ikleyn(52786) About Me 

Question 1193622: Given: △XYZ with XY ≅ XZ ≅ YZ
ZW ⊥ XY with W on XY
YZ = 8 Find: ZW
Find the measures of the following angles in degrees.
m∠WYZ =
°
m∠YWZ =
°
m∠YZW =
°
Find WY.
WY =
Find ZW. Give your answer in both simplest radical form and as an approximation correct to two decimal places.
simplest radical form ZW =

approximation ZW =

Click here to see answer by ikleyn(52786) About Me 

Question 1193820: △RST, with point D in the interior.
RG = 3, GS = 4, SH = 4, and HT = 9.
Find KT/KR

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Question 1193821: In right △ABC, m∠B = 30°. Also,
AB = 16 radical 3 and AD bisects ∠BAC
Find BD:

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Question 1193819: Given: UT bisects ∠WUV, WU = 4,UV = 14, WT = 2
Find:TV

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Question 1193593: 9/4=NP/XY=PQ/YZ=MQ/WZ
Use the equation and apply the Means-Extremes Property to find YZ.
YZ =

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Question 1193818:
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Question 1193817:
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Question 1193816:
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Question 1193850: Consider △RST, with point D in the interior.
Suppose that RG = 3, GS = 4, SH = 4, and HT = 9.
Find KT/KR

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Question 1193850: Consider △RST, with point D in the interior.
Suppose that RG = 3, GS = 4, SH = 4, and HT = 9.
Find KT/KR

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Question 1193849:
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Question 1193844:
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Question 1193845:
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Question 1193843:
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Question 1193859: Angle Z is the right angle. For the 30°-60°-90° triangle, suppose that
XY = 2a.
Find XZ and YZ

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Question 1193858: Angle C is the right angle. For the 45°-45°-90° triangle, suppose that
AB = a radical 2
Find AC and BC

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Question 1193781: Given: right △DEF with
m∠E = 2 · m∠F
and EF = 14 radical 3
Find: DE and DF in simplest radical form and approximation

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Question 1193619: Given: right △DEF with
m∠E = 2 · m∠F and EF = 14radical 3
Find: DE and DF
△D E F is given. ∠D is a right angle.
simplest radical form DE =

approximation DE =
simplest radical form DF =

approximation DF =


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Question 1193848: If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the two sides that form the bisected angle.
Given: NP = 18, MN = 27, PQ = 12, and MQ = 18;m∠P = 62° and m∠M = 36°
Find: m∠QNM in degrees

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Question 1193847: Angle C is the right angle. In right △ABC with right ∠C, AD bisects ∠BAC.
Suppose that AC = 12 and DC = 6.
Let BD = x. Then AB = 2x. Write the length of
BC as an expression involving x
Use the Pythagorean Theorem to find x. Find BD and AB.

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Question 1193846: Angle C is the right angle. In right △ABC, m∠B = 30°. Also, AB = 16 radical 3
and AD bisects ∠BAC
Find BD

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Question 1193846: Angle C is the right angle. In right △ABC, m∠B = 30°. Also, AB = 16 radical 3
and AD bisects ∠BAC
Find BD

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Question 1194105: Given: ST = 1/2 (SR) in ⊙Q
SR is a diameter
Find the following in degrees
mST°
mTR
mSTR°
m∠S°

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Question 1194105: Given: ST = 1/2 (SR) in ⊙Q
SR is a diameter
Find the following in degrees
mST°
mTR
mSTR°
m∠S°

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Question 1194108: Given: tangents AB and AC to ⊙O
m∠ACB = 72°
Find the following in degrees.
mBC°
mBDC°
m∠ABC°
m∠A°

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Question 1194107: Given: ⊙O with AB ≅ AC
m∠BOC = 84°
Find m∠ABO

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Question 1194214: Find the area in square units:
A rectangle is centered inside a larger rectangle. The area between the larger rectangle and the smaller rectangle is shaded light blue. Four lengths are given.
The bottom horizontal side of the larger rectangle is labeled 25.
The right vertical side of the larger rectangle is labeled 15.
The top horizontal side of the smaller rectangle is labeled 21.
The left vertical side of the smaller rectangle is labeled 11.

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Question 1194213: Find the area in square units
A figure consists of eight sides that are vertical or horizontal. Each pair of adjacent sides meet at a right angle. Starting with the top left corner and traveling clockwise, the sides are as follows.
The first side goes right. It is labeled 6.
The second side goes down.
The third side goes right.
The fourth side goes up. It is the same length as the second side.
The fifth side goes right. It is labeled 2.
The sixth side goes down. It is labeled 9.
The seventh side goes left. It is labeled 16. The vertical distance between this side and the third side is labeled 3.
The eighth side goes up and ends where the first side starts.

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Question 1194215: Find the semiperimeter (in inches) of a triangle whose sides measure 12 in., 17 in., and 25 in
Using Heron's Formula, find the area (in square inches) of a triangle whose sides measure 12 in., 17 in., and 25 in.
A = ? in2

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Question 1194218: In a triangle whose area is 63 in2, the base has a length of 6 in. Find the length of the corresponding altitude in inches.

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Question 1194220: Farmer Watson wishes to fence a rectangular plot of ground measuring 225 ft by 130 ft.
What amount of fencing (in feet) is needed?
What is the total cost (in dollars) of the fencing if it costs $1.69 per foot?

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Question 1194222: Find the area (in square centimeters) of a regular pentagon with an apothem of length
a = 3.6 cm and each side of length
s = 5.2 cm.
Using the formula A = 1\2 aP

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Question 1194221: Find the area (in square centimeters) of a square with apothem
a = 3.6 cm and perimeter P = 28.8 cm.

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Question 1194217: In a triangle of perimeter 72 in., the length of the first side is twice the length of the second side, and the length of the third side is 8 in. more than the length of the second side. Find the lengths of the three sides in inches.
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Question 1194217: In a triangle of perimeter 72 in., the length of the first side is twice the length of the second side, and the length of the third side is 8 in. more than the length of the second side. Find the lengths of the three sides in inches.
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Question 1194227:
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Question 1194223: Consider a regular octagon with an apothem of length
a = 9.2 in. and each side of length
s = 7.6 in
Find the perimeter (in inches) of this regular octagon.
Find the area (in square inches) of this regular octagon.

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Question 1194230: Assuming that a 90° arc has an exact length of 5𝜋 in., find the length of the radius of the circle in inches
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Question 1194230: Assuming that a 90° arc has an exact length of 5𝜋 in., find the length of the radius of the circle in inches
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Question 1194228: Find the approximate circumference (in centimeters) and area (in square centimeters) of a circle whose diameter has length 60 cm. Use 𝜋 ≈ 3.14
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