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- Find the height of the bigger building- Tan 60-1-7- Tan 35-0-7 - Let CD AB be the smaller and taller building respectively-DE - AC - 30 m

In Δ ADE nbsp; nbsp; Tan 60^∘=AE/DE=AE/30 (DE=AC=30 m) nbsp; nbsp; AE=30. Tan 60^∘=30× 1.7=51 m nbsp; nbsp; In Δ BDE nbsp; nbsp; Tan 35 ...

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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 $35^{\circ} .$ Find the height of the bigger building.

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

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

DE = AC = 30 m

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Solution

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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Two buildings on a plane ground are 20 m apart. From the top of the smaller building one can see the base of the taller building at an angle of depression of $50^{\circ}$ and its top at an angle of elevation of $25^{\circ} .$ The height of the bigger building will be $[T a n 50^{\circ} = 1.2 T a n 25^{\circ} = 0.46]$