Question
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
1.07 m
5.15 m
3.85 m
24.24 m
Answers
Answered by
GPT 3.5
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.
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.