Download MPM2D1 7.5 Solve Problems Involving Right Triangles

MPM2D1
7.5 Solve Problems Involving Right Triangles
Recall:
THE PRIMARY
TRIGONOMETRIC
RATIOS FOR ∠ A

𝒔𝒊𝒏 𝑨 =

𝒄𝒐𝒔 𝑨 =

𝒕𝒂𝒏 𝑨 =
Example 1: Solve each triangle. Round the measure of each angle to the nearest
degree. Round the length of each side to the nearest unit.
a.
b. Solve for i and j.
R
13 m
i
S
10 m
j
T
60°
8 cm
Definition of terms:
Angle of depression/ declination: angle measured below the
horizontal:
Angle of elevation/inclination: angle measured above the
horizontal:
Example 2: Kath and Yoly live in apartment buildings that are 30 m apart . The
Angle of depression from Kath’s balcony to where Yoly’s building meets the ground
is 40°.The angle of elevation from Kath’s balcony to Yoly’s balcony is 20°.
Sketch:
a) How high is Kath’s balcony above the ground, to the nearest metre?
b) How high is Yoly’s balcony above the ground, to the nearest metre?
MPM2D1
7.5 Solve Problems Involving Right Triangles
Example 3: A theodolite is an instrument used by a surveyor to measure horizontal
and vertical angles. Measurements are taken in order to find the height of a cliff
on the other side of a river, as shown. Find the height of the cliff, to the nearest
metre
Example 4: Laura is throwing a Frisbee 3 m into the air. Her sister is waiting to
catch the Frisbee 5 m away, directly below the Frisbee. What is the angle of
elevation of the path of the Frisbee?
Sketch:
Example 5: Antea wants to wash the outside windows of her house. In order to do
this, she must use a ladder. The greatest angle of elevation that is possible for
the ladder is 27°. The ladder is 3 m long. What is the maximum height that the
ladder can reach?
Sketch:
Select 10 questions
even or odd
numbers to practice
on page380-385