Right Triangle Applications



SOLUTIONS AT THE END OF PACKET

1. A regular pentagon is inscribed in a circle, shown below.

a) Find the measure of [pic] in the figure above.

b) Find the measure of side AB

c) Find the area of triangle AOB

1. A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60° with the horizontal. Approximate the height of the kite above ground level if 500 feet of string is payed out.

2. Find the area of a triangle with side lengths 5 and 8 and an included angle of 38°.

3. A person is 200 yards from a river. Rather than walking directly to the river, the person walks 400 yards along a straight path to the rivers edge. Find the acute angle ( between this path and the river’s edge.

4. A 65-foot line is used to tether a helium-filled balloon. Because of a breeze, the line makes an angle of 75( with the ground. What is the height of the balloon?

5. From an 80-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?

6. A ramp 20 feet in length rises to a loading platform that is 4 feet off the ground. What is the angle of elevation of the ramp?

7. An airplane at an altitude of 6 miles, is on a flight past that passes directly over an observer. If ( is the angle of elevation from the observer to the plane, find the distance d from the observer to the plane when a) ( = 30(, b) ( = 60(, c) ( = 120(.

8. A boat is pulled to port by means of a winch which is located on the dock 10 feet above the deck of the boat. Let X be the angle of elevation and let s be the length of the rope from the winch to the boat. a) Write X as a function of s. b) Find X when s = 48 feet and when s = 24 feet.

9. A television camera at ground level is filming the lift-off of a space shuttle at a point 750 meters from the launch pad. Let X be the angle of elevation to the shuttle and let s be the height of the shuttle. a) Write X as a function of s. b) Find X when s = 300 meters and s = 1200 meters.

10. To thank Mr. Cendrowski for the wonderful job he has done with this year’s Analysis classes, several juniors got together to erect a statue in his image and place it on the roof of the high school. A student standing 200 feet away from the building looks up at a 27( angle and notices the statue’s feet. The student then tilts her head back 15( degrees and sees the top of the statue’s head. How tall is the statue?

11. A plane flying in a straight line passes directly over point A on the ground and later directly over point B, which is 3 miles from point A. A few minutes after the plane passes over point B, the angle of elevation from A to the plane is 43˚ and the angle of elevation from B to the plane is 67˚. How high is the plane at that moment?

[pic]

1. a) 72

b) 3.53

c) 4.28

2. 437.01

3. 12.31

4. 30°

5. 62.79

6. 1526.49

7. 11.54

8. 30°, 12

60°, 6.93

120°, 6.93

9. [pic]

48, 12.02

24, 24.62

10. [pic]

300, 21.80

1200, 57.99

11. 78.18

12. 4.63

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