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Download Lesson 8-3: Trigonometry
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LESSON 8-3: TRIGONOMETRY GOAL: TO USE THE SINE, COSINE, AND TANGENT RATIOS TO DETERMINE SIDE LENGTHS AND ANGLE MEASURES IN RIGHT TRIANGLES. TRIGONOMETRIC RATIOS: SOH CAH TOA EXAMPLE 1: WRITING TRIGONOMETRIC RATIOS What are the sine, cosine, and tangent ratios for β π? sin π = πππ π = βπ¦π ππ cos π = πππ ππ = βπ¦π ππ πππ π tan π = πππ = ππ EXAMPLE 2: USING A TRIGONOMETRIC RATIO TO FIND DISTANCE In 1990, the Leaning Tower of Pisa was closed to the public due to safety concerns. The tower reopened in 2001 after a 10 year project to reduce its tilt from vertical. Engineersβ efforts were successful and resulted in a tilt of 5°, reduced from 5.5°. Suppose someone drops an object from the tower at a height of 150 ft. How far from the base of the tower will the object land? Round to the nearest foot. tan 5 = πππ π₯ = πππ 150 150 × tan 5 β ππ. ππ ππ EXAMPLE 3: USING A TRIGONOMETRIC RATIO TO FIND DISTANCE A cliff forms an angle of 84° with a lake. If you stand on the edge of the cliff and drop a rock at a height of 48 ft above the water, how far from the cliff base will the rock strike the water? Round to the nearest whole foot. tan 84 = 48 π₯ π₯ = 48 ÷ tan 84 48 ft π₯ β 5 ππ‘ 84° π₯ ππ‘ EXAMPLE 4: USING INVERSES sin β π = πππ βπ¦π 6 sin β π = 10 πβ π = sinβ1 πβ πΏ β ππ 6 10 πππ cos β π = βπ¦π cos β π = πβ π = 15 20 cosβ1 πβ πΏ β ππ 15 20 ASSIGNMENT: p 510 β 512 #βs 11 β 36 all and 39.
