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(B) Let the height of the tower be $h = 300 \,m$. Let the two trucks be at points $A$ and $B$ on the ground,and the top of the tower be $T$. The angle

Vedclass · Accepted Answer

$127$

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(B) Let the height of the tower be $h = 300 \,m$. Let the two trucks be at points $A$ and $B$ on the ground,and the top of the tower be $T$. The angles of depression are $45^{\circ}$ and $60^{\circ}$,which correspond to the angles of elevation from the trucks to the top of the tower.In $	riangle TCB$ (where $C$ is the base of the tower),$	an(60^{\circ}) = \frac{TC}{CB} \implies \sqrt{3} = \frac{300}{CB} \implies CB = \frac{300}{\sqrt{3}} = 100\sqrt{3} \approx 173.2 \,m$.In $	riangle TCA$,$	an(45^{\circ}) = \frac{TC}{CA} \implies 1 = \frac{300}{CA} \implies CA = 300 \,m$.The distance between the two trucks is $AB = CA - CB = 300 - 173.2 = 126.8 \,m \approx 127 \,m$.

Two trucks are parked in the same direction of a $300 \,m$ high tower. The angles of depression of these trucks from the top of the tower are found to be $45^{\circ}$ and $60^{\circ}$. Find the distance between these two trucks. (in $,m$)

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