A vertical pole $PQ$ has its base $Q$ on the ground. From a point $M$, 40 m from $Q$, the angle of elevation of $P$ is $a^\circ$. From another point $N$, 40$\sqrt{3}$ m from $Q$ and on the same line as $M$, the angle of elevation of $P$ is $b^\circ$. If the height of the pole is 40 m, what

Question

A vertical pole $PQ$ has its base $Q$ on the ground. From a point $M$, 40 m from $Q$, the angle of elevation of $P$ is $a^\circ$. From another point $N$, 40$\sqrt{3}$ m from $Q$ and on the same line as $M$, the angle of elevation of $P$ is $b^\circ$. If the height of the pole is 40 m, what is the value of $a^\circ + b^\circ$?

Accepted Answer

75°. From $M$, $	an a = \frac{40}{40}=1$, so $a=45^\circ$. From $N$, $	an b = \frac{40}{40\sqrt{3}}=\frac{1}{\sqrt{3}}$, so $b=30^\circ$. Therefore, $a+b=75^\circ$.

Solution

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