Geometry
Take-Home Test Chapter 8
DUE MONDAY, MARCH 29!
Name ________________________
1) The lengths of three sides of a triangle are given. Describe each triangle as acute, right, or obtuse. Show your justification.
a) 18, 80, 82
b) 6, 12, 16
2) Are the following numbers a Pythagorean Triple? Show your justification.
a) 12, 16, 27
b) 28, 53, 45
Find the values of the variables. Leave your answers in simplest radical form.
3)
4)
5)
Using the special triangles rules, find x and y. If necessary, give answers in simplest radical form.
6) x = ________
y = _________
8) x = ________ y = _______
8
7) x = _________
y = __________
9) x = _______ y = _________
11 2
y
10) Express sin T, cos T, and Tan T as ratios.
sin T = ___________
cos T = ___________
tan T = ___________
Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest degree.
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18) A surveyor measuring the tallest tree in a park is 100 ft from the tree. His angle-measuring device is 5 ft above the ground.
The angle of elevation to the top of the tree is 48o. How tall is the tree?
19) Twenty minutes after being launched, a hot-air balloon has risen to an altitude of 300m. The pilot can still see the starting
point on the ground at a 25o angle of depression. How many meters is the balloon from the starting point?
20) A captain of a sailboat sights the top of a light house at a 17o angle of elevation. A navigation chart shows the height of the
lighthouse to be 120 m. How far is the sailboat from the lighthouse?
21) Students in a hang gliding class stand on the top of a cliff 70 m high. They watch a hang glider land on the beach below.
The angle of depression to the hang glider is 72 o. How far is the hang glider from the base of the cliff?