MATH 10
TRIGONOMETRY PRE-TEST/REVIEW QUESTIONS
MULTIPLE CHOICE:
1. The length of side x is…
(a) 229.6
(b) 264.1
(c) 463.8
(d) 533.5
2. If cos θ = 0.2725, what is the value of θ to the nearest degree?
(a) 15°
(b) 29°
(c) 74°
(d) 81°
(c) 0.8391
(d) 66.42
3. Cos 40° is equal to…
(a) 0.6428
(b) 0.7660
4. opposite is the trigonometric ratio for…
adjacent
(a) sine
(b) cosine
(c) tangent
5. By using the Pythagorean theorem for right triangles, the
length of side AC, in centimeters, is…
(a) 8
(b) 12
(c) 18
(d) 65
6. A ski slope falls a vertical height of 550 metres for a
distance of 1750 m traveled down the ski hill. What is the
measure of angle θ to the nearest degree?
(a) 17°
(b) 18°
7. Calculate the value of side “x”.
c) 72°
(d) 73°
8. Find the value of the indicated angle.
9. A school soccer field measures 45 m by 65 m. To get home more quickly, John decides to
walk along the diagonal of the field. What is the angle of John’s path, with respect to the 45-m
side, to the nearest degree?
a. 55°
c. 2°
b. 34°
d. 1°
10. Which statement is incorrect?
a. You can solve for the unknown side in any triangle, if you know the lengths of the
other two sides, by using the Pythagorean theorem.
b. The hypotenuse is the longest side in a right triangle.
c. The hypotenuse is always opposite the 90° angle in a right triangle.
d. The Pythagorean theorem applies to all right triangles.
OPEN RESPONSE – Show work!
1. A roof is shaped like an isosceles triangle. The slope of the roof makes an angle of 24 with the
horizontal, and has an altitude of 3.5 m. Determine the width of the roof, to the nearest tenth of a metre.
2. A flight of stairs has a ratio of vertical distance:horizontal distance of 3:5. What angle does the flight of
stairs make with the ground, to the nearest degree?
3. A telephone pole is secured with a guy-wire as shown in the diagram. The guy-wire makes an angle of
75 with the ground and is secured 6 m from the bottom of the pole. Determine the height of the
telephone pole, to the nearest tenth of a metre.
4. In the diagram, label the hypotenuse, the opposite side, and the adjacent side relative to angle C.
5. Laura is flying a kite at a local park. She lets out 60 m of her kite string, which makes an angle of 68
with the ground. Determine the height of the kite above the ground, to the nearest tenth of a metre.
6. Kevin is standing at the top of a ladder picking apples from an apple tree. The 7-m long ladder is propped
against the tree, and makes an angle of 70° with the ground. He tosses the apples into a basket located 5.4
m from the base of the ladder, on the opposite side of the tree.
a) Determine the distance of the base of the ladder from the tree, in metres.
b) If Kevin looks down on the basket from the top of the ladder, what is the angle of depression? Answer
in degrees.
7. Matthew parks his car between Karen’s and Patrick’s apartment buildings. The car is 46 m in front of
Karen’s apartment building. The angle of elevation from the car to the top of the building is 40°.
Matthew’s car is 39 m behind Patrick’s apartment building. The angle of elevation from the car to the top
of the building is 50°.
a) Determine the height of each building, to the nearest metre.
b) State which building is taller, and by how much.
8. Jose is sitting in a tree, so that his eyes are 3.2 m above the ground. When he looks down at an angle of
depression of 42°, he can see his cat sitting in the yard.
a) Draw a diagram of the situation.
b) Determine the horizontal distance, to the nearest tenth of a metre, from the base of the tree to Jose’s
cat.
9. Myriam is participating in a water skiing competition. She goes over a water ski ramp that is 4.0 m long.
When she leaves the ramp, she is 1.7 m above the surface of the water.
a) What is the horizontal length of the ramp along the surface of the water, to the nearest tenth of a metre?
b) Determine the angle of elevation of the ramp, to the nearest degree.