Question 679894: Suppose a tree casts a shadow that is 50 feet long on level ground. If the angle formed by the ground and the light coming just over the top of the tree is 20 degrees, how tall is the tree. (Assume the tree is growing straight up out of the ground.) Please draw a diagram, write out an equation which uses an appropriate trig function, and solve for the height of the tree.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose a tree casts a shadow that is 50 feet long on level ground. If the angle formed by the ground and the light coming just over the top of the tree is 20 degrees, how tall is the tree. (Assume the tree is growing straight up out of the ground.) Please draw a diagram, write out an equation which uses an appropriate trig function, and solve for the height of the tree.
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Draw the picture.
You have a right triangle with base = 50, height = x, and angle
opposite height = 20 degrees.
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Equation:
tan(20) = height/base = x/50
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x = 50*tan(20) = 18.20 feet (height of the tree)
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Cheers,
Stan H.
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