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12.1 TRIGONOMETRIC FUNCTIONS IN RIGHT TRIANGLES DAY 1: 6 TRIG FUNCTIONS & FINDING SIDES ο Recall from Geometry: ο Pythagorean Theorem: a2+ b2= c2 ο SOH CAH TOA Cos = π΄πππππππ‘ π»π¦πππ‘πππ’π π Opposite πππππ ππ‘π ο Sin= π»π¦πππ‘πππ’π π Adjacent Angle tan= πππππ ππ‘π π΄πππππππ‘ ο 3 additional Trig Functions Cosecant π»π¦πππ‘πππ’π π = πππππ ππ‘π Secant = π»π¦πππ‘πππ’π π π΄πππππππ‘ Cotangent= π΄πππππππ‘ πππππ ππ‘π Example 1 ο Find the values of the six trigonometric functions for angle G. Example 2 ο In a right triangle, οA is acute and πππ§π¨ = Find the value of csc A. π . π Example 3 ο In a right triangle, οB is acute and π¬π’π§π© = Find the value of sec B. π . π Find a missing side ο Example 4: Find the length of y. Example 5 ο Solve βABC. Example 8 ο A) Find the measure of οA. Round to the nearest tenth if necessary. ο B. Find the measure of οB. Round to the nearest tenth if necessary. 208 Example 9 ο Find the measure of 27 οA. Warm up Solve βABC **Notice that angles are capital letters, and the sides opposite these angles are the same letter, but lowercase. B 14 A b 6 C Example 1 A golfer is standing at the tee, looking up to the green on a hill. The tee is 36 yards lower than the green and the angle of elevation from the tee to the hole is 12°. From a camera in a blimp, the apparent distance between the golfer and the hole is the horizontal distance. Find the horizontal distance. Example 2 The hill of the roller coaster has an angle of descent, or an angle of depression, of 60°. Its vertical drop is 195 feet. From a blimp, the apparent distance traveled by the roller coaster is the horizontal distance from the top of the hill to the bottom. Find the horizontal distance. Example 3 Mario hits a line drive home run from 3 feet in the air to a height of 125 feet, where it strikes a billboard in the outfield. If the angle of elevation of the hit was 22°, how far in the air did it travel? Example 4 ο To calculate the height of a tree in his front yard, Anand walked 50 feet from the base of the tree and used an inclinometer to measure the angle from his eye to the top of the tree, which was 62°. If Anandβs eye level is at 6 feet, about how tall is the tree? Example 5 ο At a certain time of the day a person six feet tall casts a four foot long shadow. Approximate the angle of elevation of the sun.
