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 (see the figure). Approximate the height of the kite above level ground if 700 feet of string is payed out. (Round your answer to one decimal place.)

Question

A guy wire is attached to the top of a radio antenna and to a point on horizontal ground that is 30.0 meters from the base of the antenna. If the wire makes an angle of 55°10' with the ground, approximate the length l of the wire. (Round your answer to the nearest tenth.)

A rocket is fired at sea level and climbs at a constant angle of 65° through a distance of 20,000 feet. Approximate its altitude to the nearest foot.

Answer 1

Each of these involves drawing a triangle with its base parallel to the ground, with a given angle. Then, either a side or the hypotenuse is given. If b is the base and h is the height, c is the hypotenuse, and a is the angle

tan(a) = h/b
cos(a) = b/c
sin(a) = h/c

For example, in the first problem,
(h-4)/700 = sin(60°)

In the second,
30/L = cos(55°10')

In the third,
h/20000 = sin(65°)