Question

Mr. Kelly wants to hang “icicle” Christmas lights and wants them to cover exactly from his roof to the top of his window. He really doesn’t want to get up on a ladder to measure so he decides to use some trigonometry. He walks 25 feet away from his house and measures the angle to the top of the window to be 59°. He then measures the angle to the roof to be 66°. How far will the “icicles” be?

Answer 1

To find the distance at which the "icicles" will be, we can use trigonometry. Let's denote the distance from the house to the "icicles" as x. We can use the tangent function to find the height of the window and the roof. By rearranging the equations, we can solve for x. Calculating this value, we find that x is approximately 4.108 feet.

Step-by-step explanation:

To find the distance at which the "icicles" will be, we can use trigonometry. Let's denote the distance from the house to the "icicles" as x. We can use the tangent function to find the height of the window and the roof. The tangent of the angle to the top of the window is equal to the height of the window divided by the distance from the house to the window. Using this information, we can set up the equation:

tan(59°) = height of window / x

Similarly, tan(66°) = height of roof / x

By rearranging the equations, we can solve for x:

x = height of window / tan(59°)

x = height of roof / tan(66°)

Now we just need to substitute the values. Let's assume the height of the window is 6 feet:

x = 6 / tan(59°)

Calculating this value, we find that x is approximately 4.108 feet. Therefore, the "icicles" will be approximately 4.108 feet away from Mr. Kelly's house.