Section 1.1 Revisit the Primary Trigonometric
Ratios. Name the sides that form the indicated angle.
a)
b)
c)
2. Evaluate. Round your answers to three decimal places.
a) sin 45
b) cos 60
c) tan 30
3. Find the measure of each angle to the nearest hundredth of a degree.
a) sin A = 0.8356
b) cos B = 0.2457
c) tan C = 1.8659
4. Solve the right triangle.
5. a) Find the measure of side q to the nearest
tenth of a metre.
b) Find the measure of P.
c) Find the measure of Q.
6. Solve the right triangle.
7. A ladder is resting against a tree. The foot of the ladder is 2 m from the base of the tree.
The ladder forms a 48 angle with the ground. How far up the tree does the ladder reach, to
the nearest tenth of a metre?
8. Find the measures of sides x and y to the nearest tenth of a metre.
Section 1.2 Solve Problems Using
Trigonometric Ratios
1.Explain each term in your own words.
a) angle of elevation
b) angle of depression
2. A 5-m ladder is resting against a wall. The base of the ladder is 2 m along the ground from the
base of the wall. What angle does
the base of the ladder make with the ground? Express your answer to the nearest tenth of a
degree.
3. An 80-m tower is supported by a guy wire attached to the top of the tower. If the wire forms
an angle of elevation of 79, how long is it? Express your answer to the nearest tenth of a
metre.
4. Jason is flying his kite. He lets out 63 m of string and the wind takes his kite up to a point
where the angle of elevation of the kite is 58. Find the altitude of the kite to the nearest
metre.
5. The ancient Greek mathematician Talis used trigonometry to find the slant side length of the
face of the Great Pyramid of Giza. An archeologist wants to replicate Talis's calculations. She
measures the base length along one side of the pyramid to be 230 m and the angle of elevation
of the side to be 52. Calculate the slant side length.
6. The highest point along a cliff is 80 m above the lakeshore. A surveyor stands on the top of
the cliff, looking through a 1.5 m tall transit instrument. He spots a boat out on the lake, at an
angle of depression of 38. How far, to the nearest tenth of a metre, is it from the boat to the
base of the cliff?
7. Michael stands 10.0 m from the base of a building. He measures the angle of elevation to the
top of the building to be 65.0. Michael’s measurement was made from 1.5 m above the
ground. Determine the height of the building to the nearest metre.
8. A search and rescue helicopter is flying at an altitude of 500 m. As it passes over a field, the
pilot spots a campfire at an angle of depression of 23.5. If the helicopter were to land in the
field directly below it, how far would the crew have to travel to reach the campfire?
Section 1.3 The Sine Law
1. State the sine law in two different forms.
2. Find the measure of C, to the nearest tenth of a degree.
a)
b)
c)
3. Find the measure of the indicated side, to the nearest tenth.
a)
b)
c)
4.
Explain why the triangle cannot be solved using the sine law.
5. Solve each triangle. Round your answers to the nearest unit, if necessary.
a) ABC, given B = 57, C = 72, and
b = 18 m.
b) DEF, given D = 66, F = 39, and
e = 10 ft.
c) GHI, given G = 72, g = 15 cm, and
h = 8 cm.
6. Find the perimeter of isosceles ABC, to the nearest inch.
7. Find the length of side AB to the nearest tenth of a metre.
8. Two guy wires 27 m and 15 m in length are to be fastened to the top of a TV tower from two
points B and C as shown. The angle of elevation to the top of the tower of the longer wire is
32.
a) How far apart are points B and C?
b) How tall is the tower?
9. The longest side of a triangle is 33 ft. Find the lengths of the other two sides to the nearest
foot.
10.
a) Use the sine ratio to find the value of x,
to the nearest tenth.
b) Use the sine law to find the value of x, to
the nearest tenth.
c) Explain why the two methods are
equivalent for a right triangle.
Section 1.4 The Cosine Law
1.
Given ABC, write the cosine law for each side in the triangle.
2. Given ABC, write the cosine law for each angle in the triangle.
3. Find the measure of the marked angle. Express your answer to the nearest degree.
a)
b)
c)
4. Find the measure of the unknown side, to the nearest tenth of a unit.
a)
b)
c)
5. Solve ABC given A = 52,
AC = 26. 2 cm, and AB = 18.8 cm.
6. Solve ABC given a = 9 cm, b = 7 cm, and
c = 8 cm.
7. A radar station located at point A is tracking ships at points B and C. How far apart are the
two ships, to the nearest tenth of a kilometre?
8. In parallelogram ABCD, the length of AB is 4 cm and the length of BC is 9 cm. If B is
54, how long is each diagonal, to the nearest tenth of a centimetre?