To secure a 618 meter radio tower against high winds, guy wires are attached to a ring 10 meters from the top of the tower. Each wire is anchored 90 meters from the base of the tower. Find the measure of the angle the wire makes with the ground. Round your answer to the nearest tenth. anybody know how to set this up?
The angle is θ, where
tanθ = (618-10)/90
To solve this problem, we can use trigonometry. Let's break down the problem and set it up step by step.
1. Draw a diagram: Visualize the radio tower with the guy wires attached. Label the tower height, the distance from the base, and the distance from the ring to the top of the tower.
Tower height = 618 meters
Distance from base to anchor point = 90 meters
Distance from ring to top = 10 meters
___________ <- Tower
| .
| .
| . <- Wire
| .
| .
| .
| .
| .
| .
| .
| .
2. Identify the right triangle: From the diagram, we can see that a right triangle is formed by the tower, the wire, and the ground. We need to find the angle that the wire makes with the ground.
___________ <- Tower
| .
| .
| . <- Wire
| .
| .
| .
|θ .
| .
| .
| .
3. Choose a trigonometric function: Since we are given the opposite and adjacent sides of the triangle, we can use the tangent function (tan) to find the angle θ.
tangent (θ) = opposite / adjacent
4. Substitute the given values: Let's plug in the values we have into the tangent formula.
tan(θ) = 618 / 90
5. Calculate the angle: Use a calculator to evaluate the tangent function.
θ ≈ tan^(-1) (618 / 90)
This will give you the angle in radians. To convert it to degrees, multiply by (180/π).
θ ≈ (tan^(-1) (618 / 90)) * (180/π)
Round the final answer to the nearest tenth.
And that's how you can set up and solve the problem to find the measure of the angle the guy wire makes with the ground.