Advanced Algebra with Trigonometry



Advanced Algebra with Trigonometry NAME ____________________

Ch 5: “Trigonometric Functions” DATE __________ PER _____

“Applications Involving Right Triangles”

Angle of Elevation: an angle measured above the line of sight

Angle of Depression: an angle measured below the line of sight

EX1] From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree

is [pic]. 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 [pic]. 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 [pic].

From a point 17.5 meters further from the space shuttle, the angle of elevation is [pic].

Find the height of the space shuttle.

Review:

1. Complete the table below. (Try not looking at your notes!)

| [pic] | [pic] | [pic] | [pic] | [pic] | [pic] | [pic] |

| [pic] | | | | | | |

| | | | | | | |

| [pic] | | | | | | |

| | | | | | | |

| [pic] | | | | | | |

| | | | | | | |

| [pic] | | | | | | |

| | | | | | | |

| [pic] | | | | | | |

| | | | | | | |

2. Find a coterminal angle for:

a) [pic] b) [pic]

3. Find the EXACT value of the 6 trig functions of the angle [pic] given in the figure.

[pic]__________ [pic]__________

[pic]__________ [pic]__________

[pic]__________ [pic]__________

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

[pic]__________ [pic]__________

[pic]__________ [pic]__________

[pic]__________ [pic]__________

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 [pic] 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 [pic]. 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 [pic]. 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 [pic]. Find the height of the aqueduct.

#5 Let [pic] be an acute angle of a right triangle for which [pic].

a) Find [pic].

b) Find [pic].

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

__________ 6) [pic]

__________ 7) [pic]

__________ 8) [pic]

__________ 9) [pic]

__________ 10) [pic]

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

__________ 11) [pic] __________ 12) [pic]

-----------------------

[pic]

[pic]

[pic]

[pic]

line of sight

angle of depression

angle of elevation

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