MCT4C1 – Unit 4
Day 1: Trigonometric Ratios
The sine ratio, the cosine ratio and the tangent ratio are always based on the chosen angle.
sinA =
hypotenuse
cosA =
adjacent
tanA =
Memory aid:
Example 1: Find A.
a)
b)
C
B
12cm
C
20cm
A
B
3cm
A
5cm
Example 2: For each triangle, pick the appropriate angle and solve for x.
a)
x
29o
5cm
b)
60o
x
7.5cm
opposite
MCT4C1 – Unit 4
To solve a triangle means to find all the unknown sides and unknown angles. In a right triangle, you
can use the primary trigonometric ratios, Pythagorean Theorem, and sum of inside angles (add up to
180°).
Example 3: Solve ABC . Find side lengths to the nearest tenth of a centimetre and angles to the
nearest degree.
11 cm
A
B
13 cm
C

The angle of elevation is the angle of view from the horizontal up to the
object being viewed. In the given diagram, x is the angle of elevation.

The angle of depression is the angle of view from the horizontal down to the object
being viewed. In the given diagram, x is the angle of depression.
MCT4C1 – Unit 4
Example 4: A surveyor is at the top of one side of a gorge. The angle of depression from there to the
base of the opposite side of the 300-m wide gorge is 31.5°. How deep is the gorge?
Example 5: Find BC to the nearest centimetre.
Example #6: Find XY to the nearest tenth of a centimetre.
MCT4C1 – Unit 4
Homework – Day 1: Primary Trigonometric Ratios
1. Solve each triangle. Round each side length to the nearest unit and each angle to the nearest degree.
2. Solve each triangle. Round each side length to the nearest tenth of a unit and each angle to the
nearest tenth of a degree
3.
MCT4C1 – Unit 4
3. Solve each triangle. Round answers to the nearest tenth, if necessary.
a. In Δ XYZ, angle X = 90o , x = 9.5cm, z = 4.2 cm
b. In Δ KLM, angle M = 90o , angle K = 37o, m = 12.3cm
c. In Δ ABC, angle A = 90o , angle B = 55.1o, b = 4.8 cm
d. In Δ DEF, angle E = 90o , d = 18.2 cm, f = 14.9 cm
4. Determine the measure of angle θ, to the nearest tenth of a degree.
5. Determine the length of AB, to the nearest tenth of a metre.
MCT4C1 – Unit 4
6. Determine the length of RS, to the nearest tenth of a centimetre.
7. Determine the length of FH, to the nearest tenth of a metre.
8. Determine the length of RT, to the nearest centimetre.
MCT4C1 – Unit 4
9. Determine the length of MN to the nearest tenth of a centimetre.
10. Find AB, to the nearest metre.
11.
Mica Dam The highest dam in Canada is the Mica Dam, one of three dams on the Columbia
River in British Columbia. From point 600m from the foot of the dam, the angle of elevation of
the top of the dam is 22o . What is the height of the dam, to the nearest metre?
12.
Surveying A surveyor measured the height of
a vertical rock face by determining the
measurements shown. If the surveyor’s
theodolite1 had a height of 1.7m, find the height
of the rock face, AB, to the nearest tenth of a
metre.
1
A precision instrument having a telescopic sight for establishing horizontal and sometimes vertical angles.
MCT4C1 – Unit 4
13.
Determine the volume of the triangular prism, to the nearest cubic centimetre.
Answers