Download 1 2 sin 30 cos30 = = = β

MA 15400
Lesson 9
Applied Trigonometric Problems
Section 6.7
This is the notation for how we label a triangle. From now on, we do not have to tell you that b is
the length of the side across from angle β, or that angle β is the measure of angle ABC.
Normally, γ will be 90°
B
β
c
a
α
A
γ
b
C
1
1
3
, sin 45° = cos 45° =
Remember that sin 30° = cos 60°= , sin 60° = cos 30° =
2
2
2
Given either one side and an acute angle or two sides of a right triangle, you can determine the other
sides and angles using the values of trig functions, 180° in a triangle, and/or the Pythagorean Thm.
The key to success in solving for the remaining pieces of a right triangle, is labeling the triangle
correctly.
Given the indicated parts of triangle ABC with γ = 90°, find the exact values of the remaining parts.
α = 30°
c = 12
a=3
β = 45°
A
30°
12
b
β
C
a
sin 30 =
cos 30 =
β=
B
β = 60°
b=8
MA 15400
Lesson 9
Applied Trigonometric Problems
Section 6.7
Given the indicated parts of triangle ABC with γ = 90° approximate the remaining parts. For angles
approximate to the nearest minute.
β = 17° 12'
a = 12.2
a=3
b=7
α = 39° 17'
c = 51
B
c
A α
β
3
C
7
3
 
α = tan −1  
7
β=
c 2 = 32 + 7 2
Given the indicated parts of triangle ABC with γ = 90°, express the third part in terms of the first
two.
α, c; b
β, b; a
MA 15400
Lesson 9
Applied Trigonometric Problems
Section 6.7
200 ft
55°
x
height
A tightrope is secured to a post that is 5 ft off the ground. The tightrope is taut and makes a 55° with
the horizontal up to the top of a pole that secures it. Approximate the height of the pole if the
tightrope is 200 feet long.
height = x + 5
5
An angle of elevation or angle of depression is the angle made with the horizontal.
angle of
depression
angle of
elevation
From the edge of a cliff, above level ground, a hiker measures the angle of depression to a friend on
the ground to be 75°. If the hiker drops his knapsack off the cliff and it lands on the ground directly
below him, approximate the height of the cliff if his friend has to walk 100 meters to retrieve it.