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The angle of elevation of the highest point of a building from two points S and T are 60^o and 30^o

The angle of elevation of the highest point of a building from two points S and T are 60^o and 30^o.T is vertically above S and ST = 10 m. Calculate the height of the building above the level S.

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$Tan \ 30^o = \frac{1}{\sqrt 3} = \frac{x}{d}$

$= x \sqrt 3$

$Tan \ 60^o = \frac{x + 10}{d}$

$\sqrt 3 = \frac{x + 10}{d}$

$d = \frac{x+ 10}{\sqrt 3}$

$x \sqrt 3 = \frac{x + 10}{\sqrt 3}$

3x = x + 10

2x = 10

x = 5

$\therefore AB,$ the height of building = 10 + 5 = 15 metres

raphael answered the question on January 20, 2017 at 06:18

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The angle of elevation of the highest point of a building from two points S and T are 60^o and 30^o

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