A ladder 20 feet long leans against the side of a house. Find the height from the top of the ladder to the ground if the angle if the angle of elevation of the ladder is 80°
To find the height from the top of the ladder to the ground, we can use trigonometry. The angle of elevation of the ladder forms a right triangle with the ground and the height of the ladder.
In this case, the ladder acts as the hypotenuse of the right triangle, the distance from the house to the base of the ladder is the adjacent side, and the height from the base of the ladder to the top is the opposite side.
We know that the length of the ladder is 20 feet, and the angle of elevation is 80°.
Using the trigonometric function tangent (tan), we can set up the equation:
tan(80°) = opposite side / adjacent side
Substituting the known values into the equation:
tan(80°) = height / 20
Now, solve the equation for the height:
height = 20 * tan(80°)
Using a calculator, find the tangent of 80°:
tan(80°) ≈ 5.6713
Now, substitute the value back into the equation for the height:
height ≈ 20 * 5.6713
height ≈ 113.426 feet
Therefore, the height from the top of the ladder to the ground is approximately 113.426 feet.