Height of the House
A pole of 8-feet height is located on top of a house, right on the edge of the ceiling. From a point on the ground, the angle of elevation to the top of the house is
and the angle of elevation to the top of the pole is
Find the height of the house.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let h be the height of the house and x be the distance between the house and the point on a ground. Then we have,
tan 21.8 = (8+h)/x and tan 17 = h/x implying, x=h/tan17 substituting which into tan 21.8 = (8+h)/x gives
tan21.8 = tan17 * (8+h)/h
tan21.8 - tan17 =8tan17/h
h/8tan17 = 1/(tan21.8 - tan17)
h = 8tan17/(tan21.8-tan17) ~ 25.94 ft
Pls respect 'coz I don't know how to use LATEX.