Question

Two boats traveling toward a lighthouse that is 20o ft above sea level at its top. When the 2 boats and the lighthouse are collinear, the boats are exactly 250 ft apart and the boat closest to the lighthouse of 15° as shown. Find the measure of x, rounded to the nearest hundredth. (Please help !!!)

Answer 1

The measure of x=
`11.35^(\circ)`

Explanation:

We are given that

Height of tower=200ft

Distance between two boats=250 ft

From given figure

`(perpendicular\;side)/(base)=tan\theta`

`(200)/(base)=tan15^(\circ)`

`base=(200)/(tan15^(\circ))=746.55 ft`

Again ,

`(200)/(746.55+250)=tan x`

`(200)/(996.55)=tan x`

`x=tan^(-1)(0.20069)=11.35^(\circ)`

Hence, the measure of x=
`11.35^(\circ)`