Name: ________________________
Chapter 7 Geometry Test Review
You should show all work on this paper for every problem.
1.)
Find the geometric mean between each pair of numbers. Answers should be in simplified radical form.
a.) 2 and 8
2.)
c.) 2 2 and 5 2
b.) 9 and 36
Find the measure of each altitude. Answers should be in simplified radical form.
a.)
b.)
3.)
Find x, y, and z. Answers should be in simplified radical form.
4.)
Determine whether each set of measures can be the measures of the sides of a right triangle. Then state
whether they form a Pythagorean Triple.
12, 16, 20
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5.)
Find x.
a.)
b.)
6.)
Find x.
a.)
b.)
c.)
x
19
d.)
x
12
7.)
The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the
hill, how high is the hill? Round your answer to the nearest tenth.
8.) The angle of depression from a balloon on a 75-foot string to a person on the ground is 36°. How high is
the balloon? Round your answer to the nearest tenth.
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9.) The tailgate of a moving van is 3.5 feet above the ground. The loading ramp is attached to the end of the van
at a 10 degree angle. Find the length of the ramp to the nearest foot.
10.) A ship determines the angle of depression to a shipwreck on the ocean floor is 13.25º. The depth chart
shows that the ocean floor is 40m below the surface. How far does the diver have to go in order to reach the
shipwreck.
9.) Use ∆PQR to find sin P, cos P, tan P, sin Q, cos Q, and tan Q. Express each ratio as a fraction.
a.) sin P =
d.) sin Q =
b.) cos P =
e.) cos Q =
c.) tan P =
f.) tan Q =
3
10.) Use your trig table or a calculator to find each value. Round to the nearest ten thousandth if necessary.
a.) sin (6) =
b.) tan (47) =
c.) cos (22) =
11.) Use your trig table or a calculator to find the measure of each angle. Round to the nearest degree if
necessary.
a.) cos (A) = 0.3846
b.) sin (X) = 0.6190
c.) tan (R) = 2.3333
12.) Find the distance, slope, and midpoint of the following: A (-5, 7) and B (3, -2)
Distance_____________
Slope ____________
Midpoint____________
13.) Find the missing sides of the triangles. Answers must be left in simplified radical form.
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14.) If
y x
 , find x when y = 2.
14 8
15.) Find the perimeter of the polygon with vertices V (3, 0), W (-2, 12), and X (-10, -3) to the nearest
tenth. Show all work to receive credit. (Hint: You need to use the distance formula).
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Use the diagram below to answer questions 15 and 16
16.) Find the length of NK and NM.
17.) Prove that <JKL is 90°.
18.) The hypotenuse of each right triangle represents a ladder leaning against a building. What is the height of
the shorter ladder (h)?
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