Question 993592: the shadow of a pole when the angle of elevation of the sun is 32° is 5m longer than the shadow of the pole when the angle of elevation of the sun is 48°. what is the length of the longer shadow of the pole?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! tan(48) = y/x
tan(32) = y/(x+5)
solve for y in both equation to get:
y = x * tan(48)
y = (x+5) * tan(32)
since they're both equal to y, the expressions on the right side of each equation must be equal to each other, so:
x * tan(48) = (x + 5) * tan(32)
simplify the right side of the equation to get:
x * tan(48) = x * tan(32) + 5 * tan(32)
subtract x * tan(32) from both sides of the equation to get:
x * tan(48) - x * tan(32) = 5 * tan(32)
simplify the left side of the equation to get:
x * (tan(48) - tan(32)) = 5 * tan(32)
divide both sides of the equation by (tan(48) - tan(32)) to get:
x = (5 * tan(32)) / (tan(48) - tan(32))
solve for x to get:
x = 6.432096215
that's your solution.
x + 5 must therefore be equal to 11.432096215
now that you know the value of x and x + 5, you can use that information to solve for y.
it should be the same in both cases.
if y = x * tan(48), then y is equal to 6.432096215 * tan(48) which is equal to 7.143566553.
if y = (x + 5) * tan(32), y is equal to 11.43209621 * tan(32) which is equal to 7.143566553.
y is the same in both cases, as it should be.
your solution is that the length of the longer shadow of the pole is 6.432096215 + 5 = 11.432096215
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