Geometry
Chapter 11 Test
Name _____________________________
Without using trigonometric ratios, find the EXACT value of n in each of the following
figures. Show your work and circle your final answer.
1.
2.
3.
4.
5. Find the EXACT values of sin 45 and tan 60.
6. List four primitive Pythagorean Triples.
7. Find the value of x using Pythagorean Triples. Be sure to show appropriate work.
8. Estimate cos 72 to the nearest hundredth.
Solve for x in each figure by using a trigonometric ratio. Express each answer to the
nearest tenth. Show your work and circle your final answer.
9.
10.
11.
12.
13. Of angles 1-3 in DEF, which has the least sine? Explain your answer.
14. Draw a diagram that shows an angle of depression. Clearly label the angle.
15. Amy is flying her kite in the park. While she holds one end of the 60-foot kite string,
the kite floats at an angle of elevation of 40. Amy’s hand is 5 feet above the ground.
How high above the ground is her kite? Draw a diagram and show your work. Round to
the hundredths place.
16. Name the similar triangles in this figure.
DEF ~ ________ ~ ________
17. Find the perimeter of this trapezoid. Leave your answer in simple radical form.
18. A 34-foot ladder is leaning against a vertical wall. The bottom of the ladder is 16
feet from the base of the wall. If the top of the ladder slides 10 feet down the wall, how
far will the bottom of the ladder slide? Leave your answer in simple radical form.
BONUS: (Do only if you have time after completing the rest of the test!)
Two observers 1600 meters apart on a straight, flat road measure the angles of elevation
of a helicopter hovering over the road between them. If these angles are 32.0 and 50.5,
how high is the helicopter?