The angles of depression of two boats A and B | vedclass

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Question

(C) Let $h$ be the height of the lighthouse. Let $d_A$ and $d_B$ be the distances of boats $A$ and $B$ from the base of the lighthouse respectively.Fr

Vedclass · Accepted Answer

The distance of $A$ is greater than $B$.

Vedclass · Answer

(C) Let $h$ be the height of the lighthouse. Let $d_A$ and $d_B$ be the distances of boats $A$ and $B$ from the base of the lighthouse respectively.From the given angles of depression,the angles of elevation from the boats to the top of the lighthouse are $25^{\circ}$ and $40^{\circ}$ respectively.Using the tangent ratio: $	an(25^{\circ}) = \frac{h}{d_A}$ and $	an(40^{\circ}) = \frac{h}{d_B}$.Since $	an(40^{\circ}) > 	an(25^{\circ})$,it follows that $\frac{h}{d_B} > \frac{h}{d_A}$.Therefore,$d_A > d_B$. Thus,the distance of boat $A$ from the lighthouse is greater than the distance of boat $B$.

The angles of depression of two boats $A$ and $B$ from the top of a lighthouse are $25^{\circ}$ and $40^{\circ}$ respectively. Then $\ldots \ldots \ldots \ldots$ from the lighthouse.

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