A vertical lookout tower has base $B$ and top $T$. Observation posts $P$ and $Q$ lie on the

Question

A vertical lookout tower has base $B$ and top $T$. Observation posts $P$ and $Q$ lie on the same straight, level path from $B$. $P$ is between $B$ and $Q$, $PQ=35\text{ m}$, and the angles of elevation of $T$ from $P$ and $Q$ are $31^\circ$ and $18^\circ$, respectively. Give non-exact numerical answers correct to $3$ significant figures. Find $BP$.[3] Find the height $BT$.[2] Find $QT$.[2]

Accepted Answer

(a) $41.2\text{ m}$ (b) $24.8\text{ m}$ (c) $80.1\text{ m}$

Hill lookout and observation posts

Hill lookout and observation posts

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