1. 14-3 Right Triangles and Trigonometric Ratios
Today’s Objective:
I can solve problems using trigonometric ratios.

2. Trigonometric Ratios for a Right Triangle
opp
hyp
sin 𝜃 =
csc 𝜃 =
opp
hyp
hypotenuse
hyp
opposite
adj
sec 𝜃 =
cos 𝜃 =
adj
hyp θ
adj
opp
cot 𝜃 =
tan 𝜃 =
adjacent
opp
adj
In ∆ABC, ∠𝐶 is a right angle and sin 𝐴 = 5 13 , find cos A, cot A and sin B. 12
cos 𝐴 = B 13
𝟓 𝟐 +
𝒃 𝟐 =
𝟏𝟑 𝟐 13 12 5
cot 𝐴 =
𝒃 𝟐 =𝟏𝟒𝟒 5 A
𝒃=𝟏𝟐 12 C 12
sin 𝐵 = 13

3. Trigonometric Ratios for a Right Triangle
In ∆ABC, ∠𝐶 is a right angle and a = 5 and c = 13, what is 𝑚∠𝐵? B 5
𝐵= cos −1 𝟓 𝟏𝟑 13
cos 𝐵 = 13 5 A C 𝐵≈
67°
What is 𝑚∠𝐴 ? 4 B
sin 𝐴 =
𝐴= sin −1 𝟒 𝟏𝟎 10 10 4 A C 𝐴≈
24°

4. The largest glass pyramid at Louvre in Paris has a square base
The largest glass pyramid at Louvre in Paris has a square base. The angle formed by each face and the ground is 49.7°.
How high is the pyramid? 𝑥
tan =
49.7°
17.5
𝑥=17.5⋅ tan 49.7°
≈20.6 m
What is the distance from the center of the base to the top?
≈27.1 m
What is the distance from a corner of the base to the top?
≈32.2 m

5. An airplane’s angle of descent into the airport is 3°
An airplane’s angle of descent into the airport is 3°. If the airplane begins its descent at an altitude of 5000 feet, what is its straight-line distance to the airport in miles?
5000
sin = 3° 𝒙
𝒙= sin 3°
≈95,500 feet
≈18 miles 3°
5000 feet
p. 924: 7-23 odds, 18 3°

6. You must build a wheelchair ramp so the slope is not more than 1 inch of rise for every 1 foot of run. What is the maximum angle that the ramp can make with the ground to the nearest tenth of a degree? 1
tan 𝜃 = 12
𝜃= tan −
≈4.8°
An entrance to a building is not wheelchair accessible. The entrance is 6 feet above ground and 30 feet from the roadway. How long must the ramp be?
72 feet