At a point on the ground 125 ft from the base of a tower, the angle of elevation to the top of the tower has a degree measure of 38 degrees. How high is the tower
Right triangle
tan of 38 = x/125
Find the tan of 38 and multiply by 125 to get your answer.
To find the height of the tower, we can use trigonometry.
Step 1: Draw a diagram to visualize the problem.
Let's draw a right triangle to represent the situation. Label the top of the tower as point T, the bottom of the tower as point A, and the point on the ground as point B.
Step 2: Identify what is given in the problem.
- The distance from point A to point B is 125 ft.
- The angle of elevation from point B to point T is 38 degrees.
Step 3: Determine which trigonometric ratio to use.
We have the opposite side (height of the tower) and the adjacent side (distance from point A to point B), so we can use the tangent function.
Tangent (θ) = opposite / adjacent
Step 4: Set up the equation and solve for the height.
tan(38 degrees) = height / 125 ft
To find the height, multiply both sides by 125 ft:
height = tan(38 degrees) * 125 ft
Using a calculator, we find:
height ≈ 91.37 ft
Therefore, the height of the tower is approximately 91.37 ft.
To determine the height of the tower, we can use trigonometry. We have the distance from the base of the tower to the point on the ground (125 ft) and the angle of elevation to the top of the tower (38 degrees).
Let's assume that the height of the tower is represented by 'h' ft.
In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to 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 to the point on the ground (125 ft).
Therefore, we have the following equation:
tan(38 degrees) = h / 125.
To find the value of h, we can rearrange the equation:
h = tan(38 degrees) * 125.
Now, let's calculate the height of the tower:
h = tan(38 degrees) * 125.
Using a calculator:
h ≈ 0.781 * 125.
h ≈ 97.625 ft.
Therefore, the height of the tower is approximately 97.625 ft.