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

Answer:

The measure of x=$11.35^{\circ}$

Step-by-step explanation:

We are given that

Height of tower=200ft

Distance between two boats=250 ft

From given figure

$\frac{perpendicular\;side}{base}=tan\theta$

$\frac{200}{base}=tan15^{\circ}$

$base=\frac{200}{tan15^{\circ}}=746.55 ft$

Again ,

$\frac{200}{746.55+250}=tan x$

$\frac{200}{996.55}=tan x$

$x=tan^{-1}(0.20069)=11.35^{\circ}$

Hence, the measure of x=$11.35^{\circ}$