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Warm-Up 8/14. Find the measure of . 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. . 4-1b Right Triangle Trigonometry. - PowerPoint PPT Presentation
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Warm-Up 8/14Find the measure of .
𝜃=𝑐𝑜𝑠−1( 512 )𝜃≈65 °
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.
4-1b Right Triangle Trigonometry
s 𝑖𝑛30= 𝑥2𝑥¿12
TX p222
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
Example 6: The chair lift at a ski resort rises at an angle of 20.75° 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 𝑖𝑛𝜃=𝑜𝑝𝑝h𝑦𝑝
s∈20.75=1200𝑑
𝑑 ∙ s∈20.75=1200𝑑 ∙𝑑
𝑑 ∙ s∈20.75=1200 The chair lift travels about 3387 feet up the side of the mountain.
𝑑=3387.045878
𝑑=1200sin 20.75
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 61° and 63°, respectively. If the canyon is 1250 feet deep, how wide is the river?
61°
61°
63°
63°
1250 ftx ft y ft
𝑡𝑎𝑛𝜃=𝑜𝑝𝑝𝑎𝑑𝑗
tan 63=1250𝑥
𝑥 ∙ tan 63=1250
𝑥=1250tan 63
tan 61=1250𝑥+𝑦(𝑥+𝑦 )∙ tan 61=1250
𝑥+ 𝑦=1250tan 61
1250tan 63 +𝑦=
1250tan 61
𝑦=1250tan61 − 1250
tan 63
𝑦 ≈55.979
The river is about 56 feet wide.
√−1math!
4-1b Assignment: TX p228-229, 42, 45, 56, 57-69 odd
Quiz Tomorrow :-)