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

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

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°

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

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= 5000 sin 3° ≈95,500 feet ≈18 miles 3° 5000 feet p. 924: 7-23 odds, 18 3°

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 −1 1 12 ≈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