Advanced Algebra with Trigonometry

Advanced Algebra with Trigonometry NAME ______Ch 5: “Trigonometric Functions” DATE ______PER _____

“Applications Involving Right Triangles”

angle of elevation Angle of Elevation: an angle measured above the line of sight line of sight Angle of Depression: an angle measured below the line of sight angle of depression

EX1] From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 64.3 . Find the height of the tree to the nearest foot.

EX2] From a 60 foot observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression of the boat is 3 . How far is the boat from the shoreline?

EX3] An observer notes that the angle of elevation from point A to the top of a space shuttle is 27.2. From a point 17.5 meters further from the space shuttle, the angle of elevation is 23.9. Find the height of the space shuttle. Review: 1. Complete the table below. (Try not looking at your notes!)

 sin cos tan csc sec cot

0 , 0

 30 , 6

 45 , 4

 60 , 3

 90 , 2

2. Find a coterminal angle for: -7p 29p a) b) 3 6

3. Find the EXACT value of the 6 trig functions of the angle  given in the figure.

cos  ______sec  ______7p q = 6 sin  ______csc  ______

tan  ______cot  ______

4. What if you’re not on the Unit Circle? Find the EXACT value of the 6 trig functions of the angle  given in the figure.

cos  ______sec  ______15 7 sin  ______csc  ______ tan  ______cot  ______Advanced Algebra with Trigonometry NAME ______Ch 5: “Trigonometric Functions” DATE ______PER _____ HOMEWORK “Applications Involving Right Triangles”

1) Television screens are measured by the length of the diagonal of the screen. Find the width of a 19-inch television screen if the diagonal makes an angle of 38 with the base of the screen.

2) The angle of elevation from a point 116 meters from the base of the Eiffel Tower to the top of the tower is 68.9 . Find the approximate height of the tower.

3) Venus rotates in a nearly circular orbit around the sun. The largest angle formed by Venus, Earth, and the sun is 46.5. The distance from Earth to the sun is approximately 149,000,000 kilometers. What is the orbital radius r of Venus? Round the answer to the nearest million kilometers.

4) From a point 300 feet from the base of a Roman aqueduct in southern France, the angle of elevation to the top of the aqueduct is 78 . Find the height of the aqueduct. 24 #5 Let  be an acute angle of a right triangle for which cot  . 7 a) Find sin .

b) Find sec .

#6-10 Find the EXACT value of each expression.

______6) sin 45  cos 60

______7) csc60sin 30  cot 45

  ______8) csc  cos 6 3

5 5 ______9) cos  sin 6 3

11 7 ______10) sin  tan 6 4

#11-12 Convert radians to degrees or degrees to radians.

7 ______11) 200 ______12) 12