Colleen is helping decorate for homecoming week. She places the ladder against the wall at a safe angle. The ladder is 12 feet long and the base of the ladder is 3 feet away from the wall.What angle, in degrees, does the ladder make with the ground? Round to the nearest tenth. a bNone of these choices are correct. c dtan-1
Question
Colleen is helping decorate for homecoming week. She places the ladder against the wall at a safe angle. The ladder is 12 feet long and the base of the ladder is 3 feet away from the wall.What angle, in degrees, does the ladder make with the ground? Round to the nearest tenth. a bNone of these choices are correct. c dtan-1
Solution
To find the angle that the ladder makes with the ground, we can use the tangent function in trigonometry. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the length of the ladder is the hypotenuse of the triangle, the distance from the wall to the base of the ladder is the adjacent side, and the height of the triangle (which we don't need for this calculation) would be the opposite side.
The formula to find the angle (let's call it θ) is:
tan(θ) = opposite/adjacent
But we want to find the angle when we know the adjacent side (3 feet) and the hypotenuse (12 feet). So we will use the inverse tangent function, or arctan, which is often written as tan^-1. This gives us:
θ = tan^-1(opposite/adjacent)
Plugging in the given values:
θ = tan^-1(3/12)
Now, use a calculator to find the arctan of 3/12. Make sure your calculator is set to give the result in degrees, not radians.
The result is approximately 14.0 degrees, rounded to the nearest tenth. So, the ladder makes an angle of 14.0 degrees with the ground.
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