How long is a ladder that reaches a height of 5.04 m at an angle of elevation of 78°?
1.07 m
5.15 m
3.85 m
24.24 m
To find the length of the ladder, we need to use the trigonometric function tangent.
In this case, the height (opposite side) is given as 5.04 m and the angle of elevation is given as 78°.
The tangent function is defined as the opposite side divided by the adjacent side.
tan(angle) = opposite/adjacent
tan(78°) = 5.04/adjacent
To find the adjacent side, we rearrange the equation:
adjacent = opposite / tan(angle)
adjacent = 5.04 / tan(78°)
adjacent ≈ 1.06 m
Therefore, the length of the ladder is approximately 1.06 m. The closest option is 1.07 m.