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°
ANS: 19.7
sin(80) = o/20
o = 19.7
20*cos80
= 3.47
To find the height from the top of the ladder to the ground, we can use trigonometry. The angle of elevation of the ladder is the angle formed between the ground and the ladder.
Let's denote the height from the top of the ladder to the ground as 'h'. We are given the length of the ladder, which is 20 feet, and the angle of elevation, which is 80 degrees.
In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. In this case, the adjacent side is 'h' and the hypotenuse is the ladder with a length of 20 feet. Therefore, the cosine of the angle of 80 degrees can be written as:
cos(80°) = h / 20
To find the value of h, we rearrange the equation:
h = 20 * cos(80°)
Using a calculator, we can evaluate the cosine of 80 degrees:
cos(80°) ≈ 0.1736
Substituting this value into the equation, we find:
h ≈ 20 * 0.1736
h ≈ 3.472 feet
So, the height from the top of the ladder to the ground is approximately 3.472 feet.