Question 993592
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