SOLUTION: 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

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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