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Chapter 5: Problem 19

A 12 -foot ladder is resting against a wall and makes an angle of \(52^{\circ}\) with the ground. Find the height to which the ladder will reach on the wall.

Short Answer

Expert verified
The ladder reaches approximately 9.56 feet on the wall.

Step by step solution

01

Identify known and unknown values

We know the length of the hypotenuse (ladder) which is 12 feet and the angle (\(52^{\circ}\)). We want to find the height of the ladder on the wall, which represents the opposite side in the triangle.
02

Choose the correct trigonometric function

Since we know the hypotenuse and we need to find the opposite side, we use the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.
03

Solve for the height

We know that \(\sin(52^{\circ}) = \frac{opposite}{hypotenuse} = \frac{Height}{12}\). Now it's a matter of solving this formula for the height. We can do this by multiplying both sides by 12, which gives us \(Height = 12 * \sin(52^{\circ})\).

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