Question

Calculate the height of the red antenna in x meters, knowing that the antenna is located on top of a 20 m high support post. Also, you know that β=6 ∘ and b=27 m. Give your answer in meters to two decimal places, but do not mark the unit. Use a decimal point. Draw an

Answer 1

To calculate the height of the red antenna, use trigonometry with the base and angle provided. The height is approximately 2.77 meters.

Step-by-step explanation:

To calculate the height of the red antenna in meters (x), we can use trigonometry and the given information.

We can set up a right triangle with the antenna height (x) as the opposite side, the base (b) as the adjacent side, and the angle (β) as one of the angles. Since we know the adjacent side (b) is 27 m and the angle (β) is 6°, we can use the tangent function to find the height (x).

Using the tangent function, we have:

tan(β) = x / b

Substituting the given values, we get:

tan(6°) = x / 27

Solving for x, we multiply both sides by 27:

x = 27 * tan(6°)

Using a calculator, we find that x ≈ 2.77 m.