Question

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.)

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°)