The angle of elevation of the top of a radio mast from a point53m from it's base on level ground is 63degrees, find the height of the mast?
tan 63 = h/53
Tan63 = h/53.
h = 53*Tan63 = ---------Meters.
Seriously this is not my question
To find the height of the mast, we can use the tangent function. Here's how you can solve it step by step:
Step 1: Draw a diagram to visualize the problem. Draw a right-angled triangle with the radio mast as the vertical side, the distance from the base of the mast to the point as the horizontal side, and the angle of elevation as the angle.
Step 2: Label the sides of the triangle. Let the height of the mast be h, the distance from the base to the point be d, and the angle of elevation be A.
Step 3: Identify the trigonometric function to use. In this case, we'll use the tangent function, which relates the angle and the ratio of the opposite side to the adjacent side.
Step 4: Write down the formula for tangent. The formula is tan(A) = opposite/adjacent.
Step 5: Plug in the values you know. We have tan(63°) = h/d.
Step 6: Rearrange the formula to solve for the height, h. Multiply both sides of the equation by d: h = d * tan(63°).
Step 7: Calculate the height. Substitute the values of d = 53m and tan(63°) ≈ 1.880726: h = 53m * 1.880726 ≈ 99.607078m.
Therefore, the height of the mast is approximately 99.6 meters.