Question

A six-foot person walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When the person is 122 feet from the tower and 3 feet from the tip of the shadow, the person's shadow starts to appear beyond the tower's shadow.

(a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities of the triangle and use a variable to indicate the height of the tower.

(b) Use a trigonometric function to write an equation involving the unknown quantity h.
(c) What is the height of the tower?

Answer 1

b.
`tan(\alpha)= (h)/(122+3)`

c.

`tan(\alpha)=(h)/(122+3) = (6)/(3) \\ \\ (h)/(125) = 2 \\ \\h=250`