p a radio mast from a point 53 metres from its base on level ground is 61 degrees.What is the height of the mast to the nearest 5 metres
To find the height of the mast, we can use trigonometry and the concept of tangent.
Tangent is defined as the ratio of the length of the side opposite an angle to the length of the adjacent side. In this case, the height of the mast is the opposite side, and the distance from the base is the adjacent side.
We can use the tangent formula: tan(angle) = opposite/adjacent
In this problem, the angle is 61 degrees, and the distance from the base is 53 meters.
tan(61°) = opposite/53
To get the height of the mast, we rearrange the formula to solve for the opposite side:
opposite = tangent(angle) * adjacent
opposite = tan(61°) * 53
Using a calculator, we find:
opposite ≈ 86.72 meters
Therefore, the height of the mast is approximately 86.72 meters to the nearest 5 meters.