Question

Find x. Round your answer to the nearest tenth of a degree. A right triangle labeled A B C and A C B is a right angle. Segment A B is 27, and segment C B is labeled 18, and angle A B C is labeled x degrees. Type your numerical answer (without units) below.

Answer 1

To find the value of angle ABC (labeled x degrees), we can use the trigonometric function tangent (tan).

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, we have the side opposite angle ABC as 27 (segment AB) and the side adjacent to angle ABC as 18 (segment CB).

Using the tangent function, we can set up the following equation:

tan(x) = opposite/adjacent

tan(x) = 27/18

Now, we can solve for x by taking the inverse tangent (arctan) of both sides:

x = arctan(27/18)

Using a calculator, we find:

x ≈ 55.6 degrees

Rounding to the nearest tenth of a degree, x is approximately 55.6 degrees.