Trigonometric Ratios Worksheet Page 11
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221.4 Solving Problems Using Primary Trigonometric Ratios
KEY CONCEPTS
• The primary trigonometric ratios can be used to solve problems that involve right
triangles.
• Problems involving right triangles in two dimensions and in three dimensions can be
solved using the Pythagorean theorem and/or the primary trigonometric ratios.
Example
From an army tank, the angle of elevation to the top of a 15-m tower is 15�. �fter advancing
�. �fter advancing
. �fter advancing
toward the tower, the angle of elevation is 25�. How far did the tank advance�
�. How far did the tank advance�
. How far did the tank advance�
Solution
Sketch and label a diagram.
15 m
25°
15°
X
B
A
Write an expression for the initial distance from the tank to the tower, �X.
15
____
tan 15� � =
�X
15
_______
�X =
tan 15� �
Write an expression for the new distance from the tank to the tower, BX.
15
____
tan 25� � =
BX
15
_______
BX =
tan 25� �
Determine the distance the tank advanced, �X − BX.
Distance = �X − BX
15
15
_______
_______
=
−
tan 15� �
tan 25� �
= 23.8131…
≐ 23.8
The tank advanced approximately 23.8 m.
978-0-07-090893-2 Mathematics for College Technology 12 Study Guide and Exercise Book • MHR 11
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