Warm-Up 8/14Find the measure of .
π=πππ β1( 512 )πβ65 Β°
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 ππ30= π₯2π₯ΒΏ12
TX p222
Applications:- Line of sight: line from observerβs 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 20.75Β° 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 πππ=πππhπ¦π
sβ20.75=1200π
π β sβ20.75=1200π βπ
π β sβ20.75=1200 The chair lift travels about 3387 feet up the side of the mountain.
π=3387.045878
π=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 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‘πππ=ππππππ
tan 63=1250π₯
π₯ β tan 63=1250
π₯=1250tan 63
tan 61=1250π₯+π¦(π₯+π¦ )β tan 61=1250
π₯+ π¦=1250tan 61
1250tan 63 +π¦=
1250tan 61
π¦=1250tan61 β 1250
tan 63
π¦ β55.979
The river is about 56 feet wide.
ββ1math!
4-1b Assignment: TX p228-229, 42, 45, 56, 57-69 odd
Quiz Tomorrow :-)