Angle of Elevation and Depression

Brian’s kite is flying above a field at the end of 65 m of string. If the angle of elevation to the kite measures 70°, how high is the kite above Brian’s head?

• 49m

• 62 m

• 61 m

• 60m

From an airplane at an altitude of 1200 m, the angle of depression to a building on the ground measures 28°. Find the distance from the plane to the building

• 2048.7

• 2172.4 m

• 3245.4 m

• 2256.9 m

From a point on the ground 12 ft from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. How tall is the flagpole?

• 15.9 ft

• 14.7 ft

• 16.4 ft

• 2.6 ft

From a plane flying due east at 265 m above sea level, the angles of depression of two ships sailing due east measure 35° and 25 °. How far apart are the ships?

• 185.4 m

• 189.9 m

• 182.7 m

• 192.3 m

A man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52 degrees . How high off the ground is the kite? How far away is the man from the spot directly under the kite? 

• Height of kite: 75 ft.; Ground distance from man to kite: 72.1 ft 

• Height of kite: 78 ft.; Ground distance from man to kite: 61.6 ft 

• Height of kite: 64 ft.; Ground distance from man to kite: 61.6 ft 

• Height of kite: 78 ft.; Ground distance from man to kite: 58.1 ft 

From the top of a vertical cliff 40 m high, the angle of depression of an object that is level with the base of the cliff is 34º. How far is the object from the base of the cliff?

• 62.0 m

• 58.7 m

• 60.1 m

• 59.3 m

An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane take off in order to avoid crashing into the building? Assume that the airplane flies in a straight line and the angle of elevation remains constant until the airplane flies over the building.

• The plane must climb at an angle greater than 19.6°

• The plane must climb at an angle greater than 15.4°

• The plane must climb at an angle greater than 16.7°

• The plane must climb at an angle greater than 21.8°

A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in order to reach the top of the wall?

• 68.2°

• 28.4°

• 78.1°

• 105.6°

One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the lengths of all three sides, to three decimal places.

• Legs: 5.3 & 11.3; Hypotenuse: 14

• Legs: 8.2 & 10.7 ; Hypotenuse: 14

• Legs: 4.1 & 11.3 ; Hypotenuse: 12

• Legs: 5.3 & 10.7 ; Hypotenuse: 12

Standing on a cliff 380 meters above the sea, Pat sees an approaching ship and measures its angle of depression, obtaining 9 degrees. How far from shore is the ship? Now Pat sights a second ship beyond the first. The angle of depression of the second ship is 5 degrees. How far apart are the ships?

• First ship: 4325 m; Second ship: 4348.1 m; Distance between ships: 1934 m

• First ship: 2399.2 m; Second ship: 4343.4 m; Distance between ships: 1944.2 m

• First ship: 2447.4 m; Second ship: 4643.4 m; Distance between ships: 1956.2 m