the angle of elevation of the top of a radio mast from a point 53m from its base on level ground is 61degre. Find the height of the mast to the nearest 5m.
h = 53*3.7432
= 198.4
Nearest 5 m? your instructor is too easy.
tan61=h/53
h=53*tan61
put this into your google search window:
53*tan(61degrees)=
Don t understand
To find the height of the mast, we can use trigonometry. Let's start by drawing a diagram to visualize the problem.
1. Draw a triangle representing the situation described:
- Label the base of the triangle as 53m (distance from the base of the mast to the observer).
- Label the height of the triangle as 'h' (height of the mast).
- Label the angle between the base and the height as 61 degrees.
Now, we can use the trigonometric function for the tangent of an angle (in this case, 61 degrees) to find the height of the mast.
2. Recall that the tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle:
tan(angle) = opposite / adjacent
In this case, the opposite side is 'h' (height) and the adjacent side is 53m. So, we can write:
tan(61 degrees) = h / 53m
3. Now, rearrange the equation to solve for 'h':
h = tan(61 degrees) * 53m
4. Calculate the height using a calculator or by looking up the tangent of 61 degrees (which is approximately 1.88). Then, multiply this value by 53m:
h = 1.88 * 53m
h = 99.64m
Rounding to the nearest 5m, the height of the mast is approximately 100m.