A tree is growing on a hillside and this hillside makes a θ=11∘ angle with the horizontal. The tree itself is growing at a right angle to the horizontal. The sun is shining and this causes the tree to cast a shadow which points up the hillside. This shadow is s=21 meters long. The angle of elevation from the tip of the shadow to the sun is ϕ=18∘. Find the height of the tree to at least four decimal places.
-
Let the foot of the tree = A,
the top of the tree = C,
the tip of the shadow = B
the height of the tree = h
angle CAB = 90 - 11 = 79°
angle ABC = 11 + 18 = 29°
angle ACB = 180 - 79 - 29 = 72°
side AB = 21 m
now use the sine rule:
AB/sin72 = h/sin29
h = 21*sin29/sin72
h = 10.7049 m
OG
the top of the tree = C,
the tip of the shadow = B
the height of the tree = h
angle CAB = 90 - 11 = 79°
angle ABC = 11 + 18 = 29°
angle ACB = 180 - 79 - 29 = 72°
side AB = 21 m
now use the sine rule:
AB/sin72 = h/sin29
h = 21*sin29/sin72
h = 10.7049 m
OG