The angle of elevation of the top of a tower from a point 42m away from its base on level ground is 36 degree find the height of a tower.
draw a diagram. You should see that
h/42 = tan36°
so now finish it off to find h.
To find the height of the tower, we can use trigonometry, specifically the tangent function.
Given:
Angle of elevation = 36 degrees
Distance from the base of the tower = 42 meters
Let's label the height of the tower as h.
Using trigonometry, we know that the tangent of an angle can be defined as the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the tower (h), and the adjacent side is the distance from the base of the tower (42 meters).
So, we can set up the equation:
tan(angle) = opposite / adjacent
tan(36 degrees) = h / 42
To find the height (h), we can rearrange the equation:
h = tan(36 degrees) * 42
Using a calculator, let's find the value of h:
h = tan(36 degrees) * 42
h ≈ 0.7265 * 42
h ≈ 30.481 meters
Therefore, the height of the tower is approximately 30.481 meters.
To find the height of the tower, we can use trigonometry.
Let's visualize the situation:
Let the height of the tower be represented by 'h'. The distance between the point on the ground and the tower's base is given as 42 meters. The angle of elevation from this point to the top of the tower is 36 degrees.
Using the trigonometric function tangent, we can establish the following relationship:
tangent(angle) = opposite/adjacent
In this case, the opposite side is the height of the tower (h), and the adjacent side is the distance between the point and the base of the tower (42 m).
Therefore, we can write the equation as:
tangent(36 degrees) = h / 42
Now, we can solve for the height, 'h'.
First, let's find the tangent of 36 degrees:
tangent(36 degrees) ≈ 0.7265 (rounded to four decimal places)
Now, we can rearrange the equation to solve for 'h':
h = tangent(36 degrees) * 42
Plugging in the values:
h ≈ 0.7265 * 42
Calculating this expression:
h ≈ 30.510 (rounded to three decimal places)
So, the approximate height of the tower is 30.510 meters.