Question

A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an angle of 74° with the level ground. How high on the wall does the ladder reach? (Round your answer to the nearest hundredth).

Answer 1

Length of the ladder = 6.5 feet
Angle = 74°

Height = 6.5 * sin(74°)

Calculating this, we find:

Height ≈ 6.5 * 0.9613 ≈ 6.24 feet

Answer 2

6.32ft

Explanation:

To find the height on the wall where the ladder reaches, we can use trigonometry and specifically the sine function.

Let's label the distance on the wall where the ladder reaches as "h." We can use the given information to set up the equation:

sin(74°) = h / 6.5

To solve for "h," we can rearrange the equation as follows:

h = sin(74°) * 6.5

Calculating this expression will give us the height on the wall where the ladder reaches:

h ≈ sin(74°) * 6.5 ≈ 6.32 feet

Therefore, the ladder reaches a height of approximately 6.32 feet on the wall.