JAMB - Mathematics (1987 - No. 31)
From two points x and y, 8m apart, and in line with a pole, the angles of elevation of the top of the pole are 30ºand 60º respectively. Find the height of the pole assuming that x, y, and the foot of the pole are on the same horizontal plane and x and y are on the same side of the pole.
\(\sqrt{6}\)
4\(\sqrt{3}\)
\(\sqrt{3}\)
\(\frac{12}{\sqrt{3}}\)
Vysvetlenie
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\(\sqrt{3}\)