Geometry
Test – Chapter 8
Name _________________________
1) The lengths of three sides of a triangle are given. Describe each triangle as acute, right, or obtuse. Show your
justification.
a)
14, 50, 48
b)
9, 7, 6
2) Is 13, 84, 85 a Pythagorean Triple? Show your justification.
Find the values of the variables. Leave your answers in simplest radical form.
3) x = ___________
4) x = ______________
5) Simplify the following radical expressions.
a)
150
3
b)
15  30


Using the special triangles rules, find x and y. If necessary, give answers in simplest radical form.
6) x = _______
y = ________
7. x = _______
y = ________
8) x = _______
y = ________
9) x = _______
y = ________
10) Express sin A, cos A, and Tan A as ratios.
Sin A = ___________
Cos A = ___________
Tan A = ___________
Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest degree.
11) x = ___________
12) x = ___________
13) x = ___________
14) x = ___________
15) x = ___________
16) x = ___________
17) Find x to the nearest tenth.
18) A forest ranger looking out from a ranger’s station can see a forest fire at a 35 o angle of depression. The ranger’s position is
100 ft above the ground. How far is it from the base of the ranger’s station to the fire?
19) A child lets out his kite string 142 ft in the air. The angle the kite string makes with the ground is 53 o. What is the height of
the kite?
20) A surveyor measures the height of a building that is 50 ft away from him. His angle-measuring device is 4 ft above the
ground. The angle of elevation to the top of the building is 63 o. How tall is the building?
21) An airplane pilot can see the top of a traffic control tower at a 20 o angle of depression. The airplane is 5000 ft from the
top of the tower. What is the altitude of the airplane if the tower is 30 ft tall?