Two towers of the same height stand on opposite sides of a road 100 m wide- At a point on the road between the towers- the elevations of the towers are 30- and 45- Find the height of the towers and the position of the point from one of the towers-A- 36-6 m and 63-4 mB- 63-6 m and 63-4 mC- 66-3 m and 63-4 mD- 36-6 m and 86-4 m

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Two towers of...

Question

Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are $30^{\circ}$ and $45^{\circ}$ Find the height of the towers and the position of the point from one of the towers:

36.6 m and 63.4 m

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63.6 m and 63.4 m

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66.3 m and 63.4 m

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36.6 m and 86.4 m

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Solution

The correct option is A
36.6 m and 63.4 m

Let the height of each building be 'h' m and let the point be at a distance of 'x' m from the one having an elevation of 30 degrees.

tan 30 = $\frac{h}{x}$ => x = 1.732 $\times$ h ---(1)
tan 45 = $\frac{h}{(100 - x)}$ => 100 - x = h
Putting the value of x from eqn (1), we get
h = 36.6 m
x = 63. 4 m

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Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are 30∘ and 45∘ Find the height of the towers and the position of the point from one of the towers:

Two towers of the same height stand on opposite sides of a road 100 m wide. At a point on the road between the towers, the elevations of the towers are $30^{\circ}$ and $45^{\circ}$ Find the height of the towers and the position of the point from one of the towers: