A cable that is used to support a 73 foot tower is secured to the fround 38ft from the base of the tower. Find the angle of elevation to the nearest degree that cable makes with the ground? Idont know how to do this? Explain?
tan Theta=38/73
Theta= arctan(38/73)=
To find the angle of elevation that the cable makes with the ground, you can use trigonometric functions.
In this case, you have a right triangle formed by the tower, the cable, and the ground. The height of the tower is 73 ft, and the horizontal distance from the base of the tower to where the cable is secured is 38 ft.
We can use the tangent function to find the angle of elevation. 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 (73 ft), and the adjacent side is the horizontal distance from the base of the tower to where the cable is secured (38 ft).
Therefore, the tangent of the angle of elevation can be calculated as:
tan(angle) = opposite/adjacent
tan(angle) = 73/38
Next, we need to solve for the angle by taking the inverse tangent (arctan or tan^(-1)) of both sides of the equation:
angle = arctan(tan(angle)) = arctan(73/38)
Using a calculator, you can find that arctan(73/38) is approximately 61.44 degrees.
Therefore, the angle of elevation to the nearest degree is approximately 61 degrees.
To find the angle of elevation, you can use trigonometry. Specifically, you can use the tangent function. Here's how you can solve this problem step-by-step:
Step 1: Visualize the problem
Imagine a right-angled triangle where the base is the distance from the base of the tower to the point where the cable is secured (38 ft), the height is the height of the tower (73 ft), and the hypotenuse is the cable itself. We need to find the angle of elevation, which is the angle between the ground and the hypotenuse.
Step 2: Apply the tangent function
The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. In our case, opposite refers to the height and adjacent refers to the base. So, the tangent of the angle of elevation (θ) can be calculated as follows:
tan(θ) = opposite / adjacent
tan(θ) = height / base
tan(θ) = 73 ft / 38 ft
Step 3: Calculate the angle
To find the value of θ, take the inverse tangent (or arctan) of the calculated value from Step 2. Use a scientific calculator or an online trigonometric calculator to find the inverse tangent of 73 ft / 38 ft:
θ = arctan(73/38)
Finally, determine the angle to the nearest degree using the calculator or round the result to the nearest whole number.
Therefore, the angle of elevation to the nearest degree that the cable makes with the ground is approximately X degrees (depending on the calculated value).