A ladder is leaning against the side of a house so that it can reach a window that is 25 feet off the ground. The angle in which is formed between the ladder and the ground is 52 degrees. How far from the base of the house is the base of the ladder? Round the answer to the nearest tenth of a foot.
TanTheta=tan52=25/h
h= 25/tan52
To find the distance from the base of the house to the base of the ladder, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the ground, and the side of the house. The angle between the ground and the ladder is 52 degrees, and the length of the ladder is 25 feet.
We can use the sine function to find the length of the side opposite the angle. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the hypotenuse is the length of the ladder.
So, the equation becomes:
sin(52 degrees) = opposite side / hypotenuse
Rearranging the equation to solve for the opposite side, we have:
opposite side = sin(52 degrees) * hypotenuse
Now we can plug in the values:
opposite side = sin(52 degrees) * 25 feet
Calculating the opposite side, we have:
opposite side ≈ 20.063 feet
Therefore, the base of the ladder is approximately 20.1 feet from the base of the house, rounded to the nearest tenth of a foot.