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Page 1: Warm-Up  8/14

Warm-Up 8/14Find the measure of .

πœƒ=π‘π‘œπ‘ βˆ’1( 512 )πœƒβ‰ˆ65 Β°

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Rigor:You will learn the six trigonometric functions and how to use them to solve problems. Relevance:You will be able to solve real world right triangle trigonometry problems using the six trigonometric functions.

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4-1b Right Triangle Trigonometry

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s 𝑖𝑛30= π‘₯2π‘₯ΒΏ12

TX p222

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Applications:- Line of sight: line from observer’s eye to object- Angle of elevation: object is above horizontal, angle between line of sight and horizontal

- Angle of depression: object is below horizontal, angle between line of sight and horizontal

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Example 6: The chair lift at a ski resort rises at an angle of 20.75Β° while traveling up the side of a mountain and attains a vertical height of 1200 feet when it reaches the top. How far does the chair lift travel up the side of the mountain?

opphyp

s π‘–π‘›πœƒ=π‘œπ‘π‘h𝑦𝑝

s∈20.75=1200𝑑

𝑑 βˆ™ s∈20.75=1200𝑑 βˆ™π‘‘

𝑑 βˆ™ s∈20.75=1200 The chair lift travels about 3387 feet up the side of the mountain.

𝑑=3387.045878

𝑑=1200sin 20.75

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Example 7: A sightseer looks down into a deep canyon using binoculars. The angles of depression to the far bank and near bank of the river below are 61Β° and 63Β°, respectively. If the canyon is 1250 feet deep, how wide is the river?

61Β°

61Β°

63Β°

63Β°

1250 ftx ft y ft

π‘‘π‘Žπ‘›πœƒ=π‘œπ‘π‘π‘Žπ‘‘π‘—

tan 63=1250π‘₯

π‘₯ βˆ™ tan 63=1250

π‘₯=1250tan 63

tan 61=1250π‘₯+𝑦(π‘₯+𝑦 )βˆ™ tan 61=1250

π‘₯+ 𝑦=1250tan 61

1250tan 63 +𝑦=

1250tan 61

𝑦=1250tan61 βˆ’ 1250

tan 63

𝑦 β‰ˆ55.979

The river is about 56 feet wide.

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βˆšβˆ’1math!

4-1b Assignment: TX p228-229, 42, 45, 56, 57-69 odd

Quiz Tomorrow :-)