From two points x and y, 8m apart, and in line with a pole, the angle of elevation of the top of the pole are 30o and 60o respectively. Fins the height of the pole assuming that x, y and the foot of the pole are the same horizontal plane and x and y are on the same side of the pole.
- \(\sqrt{6}\)
-
4\(\sqrt{3}\)
- \(\sqrt{3}\)
- \(\frac{12}{\sqrt{3}}\)
The correct answer is: B
Explanation
From < ZWY
\(\frac{h}{a}\) = Tan60º
h = a tan 60º .............................1
From < XWZ
\(\frac{h}{ 8 + a }\) = tan 30º
h = ( 8 + a ) tan 30º ...................2
equate 1 and 2
(8 + a ) tan30º = a tan60º
\(\frac{( 8 + a )}{\sqrt3}\) = a\(\sqrt{3}\)
8 + a = 3a
2a = 8
a = 4
but h = a tan 60º
= 4\(\sqrt{3}\)