From the top of a cliff 100 m high, the angles depression of two boats on opposite sides of cliff are $30^\circ$ and $60^\circ$. The distance between the boats is ______.

Question

KollegeApply · Accepted Answer

From the top of a cliff 100 m high, the angles depression of two boats on opposite sides of cliff are $30^\circ$ and $60^\circ$. The distance between the boats is 230.94 m. Explanation: Let the horizontal distances from the cliff base to the two boats be a and b. For angles of depression $30^\circ$ and $60^\circ$, tan 30^circ = 1/sqrt(3) = 100/a $\Rightarrow$ a = 100sqrt(3) tan 60^circ = sqrt(3) = 100/b $\Rightarrow$ b = 100/sqrt(3) Distance between boats = a + b = 100(sqrt(3) + 1/sqrt(3)) = 400/sqrt(3) = 230.94 m

AChoose Your Answer