Question

what is the distance from the first observation point to the top of the tower (x)? round the answer to the nearest tenth.
122.5 ft
183.7 ft
244.9 ft
501.9 ft

Explanation:

Step1: Find the height of the tower

Let the height of the tower be \( h \).
Using the right - triangle with the \( 60^{\circ} \) angle and side length \( 150\) ft:
\(\sin60^{\circ}=\frac{h}{150}\), so \(h = 150\times\sin60^{\circ}=150\times\frac{\sqrt{3}}{2}=75\sqrt{3}\)

Step2: Use the height to find \(x\)

In the right - triangle with the \( 45^{\circ} \) angle:
Since \(\sin45^{\circ}=\frac{h}{x}\), and \(h = 75\sqrt{3}\)
\(x=\frac{h}{\sin45^{\circ}}=\frac{75\sqrt{3}}{\frac{\sqrt{2}}{2}}=\frac{150\sqrt{3}}{\sqrt{2}}=\frac{150\sqrt{6}}{2}=75\sqrt{6}\approx75\times2.449 = 244.9\) (rounded to the nearest tenth)

Answer:

C. 244.9 ft