Two buildings on a plane ground are 30 m apart- From the top of the smaller building- one sees the base of the other building at an angle of depression of 60- and its top at an elevation of 35- The height of the bigger building is - an 60-1-7- T an 35-0-7 -DA- 82 mB- 52 mC- 72 mD- 62 m

The correct option is C 72 m In Δ ADE Tan 60^∘=AE/DE=AE/30 (DE=AC=30 m) AE=30. Tan 60^∘=30× 1.7=51 m In Δ BDE Tan 35^∘=BE/DE=BE/30 (DE=AC=30 ...

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Mathematics

Angle of Elevation and Angle of Depression

Two buildings...

Question

Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of $60^{\circ}$ and its top at an elevation of $35^{\circ} .$ The height of the bigger building is

$[\begin{matrix} T a n 60^{\circ} = 1.7 T a n 35^{\circ} = 0.7 \end{matrix}]$

Let CD $&$ AB be the smaller and taller building respectively.

DE = AC = 30 m

82 m

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52 m

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72 m

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62 m

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Solution

The correct option is C 72 m

In $Δ A D E$

$T a n 60^{\circ} = \frac{A E}{D E} = \frac{A E}{30} (D E = A C = 30 m)$

$A E = 30. T a n 60^{\circ} = 30 \times 1.7 = 51 m$

In $Δ B D E$

$T a n 35^{\circ} = \frac{B E}{D E} = \frac{B E}{30} (D E = A C = 30 m)$

$B E = 30. T a n 35^{\circ}$

$B E = 30 \times 0.7 = 21 m$

Height of taller building is

$A B = A E + E B = 51 m + 21 m = 72 m$

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The correct option is C 72 mIn Δ ADE Tan 60∘=AEDE=AE30 (DE=AC=30 m) AE=30. Tan 60∘=30×1.7=51 m In Δ BDE Tan 35∘=BEDE=BE30 (DE=AC=30 m) BE=30. Tan 35∘ BE=30×0.7=21 m Height of taller building is AB=AE+EB=51 m+21 m=72 m