Question

A tree standing vertically on level ground casts a 140 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 24.7°. Find the height of the tree to the nearest foot.,

Answer 1

Let the height of the tree be h foot. Trigonometric ratio for tangent = Opposite side / adjacent side----(1) Since the tree is standing vertically on a level ground, the three points, [ Top of the tree, the point where the tree touches the ground and the point where the shadow ends] form a right angled triangle. Applying (1) for the above three points, tan(24.7)=(height of the tree)/(length of shadow) Hence, height of the tree = tan(24.7)*(length of the shadow) = (0.46)*140 = 65 foot (Rounding off to the nearest foot)