The base of a vertical mast is on the same ground level with two points A and B from the point A 64m south of the mast the angle of elevation of the top of the mast is 30° B is 58m from A on a bearing of 50° find the height of the mast
To find the height of the mast, we can use trigonometry and create a right triangle using the given information.
Let's visualize the problem. We have a mast with a base point on the ground and two points A and B. Point A is 64m south of the mast, and point B is 58m from point A at a bearing of 50°.
Step 1: Draw a diagram
Draw a horizontal line to represent the ground. Label the base of the mast as point M. Plot points A and B relative to point M according to the given distances and angles.
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B---------M---------A
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Step 2: Calculate the height of the mast
We need to find the height of the mast, which is the side opposite to the angle of elevation. Let's label the height as h.
Using trigonometry, we know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the angle of elevation is 30°, and the opposite side is h, while the adjacent side is 64m.
So, we have: tan(30°) = h/64m
Step 3: Solve for h
To find h, we need to use the inverse tangent (arctan) function to isolate h.
h = 64m * tan(30°)
h ≈ 64m * 0.5774
h ≈ 36.97m
Therefore, the height of the mast is approximately 36.97 meters.