Question

a lamppost, cab, bent at point a after a storm. the tip of the lamppost touched the ground at point c, as shown below: triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet. what is the height, in feet, of the portion ab of the lamppost?

Answer 1

Answer: 20 tan 55

Explanation:

took test and got it right

Answer 2

The height of the portion AB of the lamppost is found by using the tangent of angle C is AB = 28.56 feet.

To find the height of the portion AB of the lamppost in triangle ABC, we can use trigonometric ratios since triangle ABC is a right triangle.

Given that the measure of angle C is 55 degrees, angle ABC is 90 degrees, and the length of BC is 20 feet, we can apply the tangent function which relates the opposite side AB to the adjacent side BC in a right-angled triangle.

The tangent of angle C (tan(55°)) is equal to the opposite side AB over the adjacent side BC.

Therefore, we can set up the equation tan(55°) = AB / 20.

To solve for AB, we multiply both sides by 20 feet to get AB = 20 * tan(55°).

Using a calculator, compute tan(55°) and then multiply by 20 to get the height AB. Make sure your calculator is in degree mode.

AB = 20 * tan(55°)

AB = 20 * 1.428

AB = 20 * tan(55°)

AB = 28.56 feet

The diagram is given below: