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

−1250tan 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 :-)