A man 23

A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60°, and angle of depression of the base of the hill is 30°. Find the distance of the hill from the ship and the height of the hill.

Correct answer:

x =  17.3205 m
h =  40 m

Step-by-step explanation:

$$\begin{gathered} s=10\text{m} \\ \alpha =60{}^{\circ } \\ \beta =30{}^{\circ } \\ \tan \beta =s:x \\ x=\frac{s}{\tan \beta }=\frac{s}{\tan 30°}=\frac{10}{\tan 30°}=\frac{10}{0.57735}=17.321=17.3205\text{m} \end{gathered}$$

$$\begin{gathered} \tan \alpha =y:x \\ y=x\cdot \tan \alpha =x\cdot \tan 60°=17.3205\cdot \tan 60°=17.3205\cdot 1.732051=30 \\ h=s+y=10+30=40\text{m} \end{gathered}$$

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