Question

Kiera is sketching a logo design for a client. The client wants the logo to be her initials inside of a right triangle. The right triangle has a base length of four inches and a height of two inches, with the right angle on the left and between the two measurements. What is the approximate angle measure of the angle formed at the top of the triangle logo? Round your answer to the nearest whole degree.(1 point)

Answer 1

To find the angle at the top of the right triangle, we can use the tangent function which relates the angle to the opposite side and the adjacent side.

Given:

• The height of the triangle (opposite side) = 2 inches
• The base of the triangle (adjacent side) = 4 inches

We can find the angle at the top of the triangle, let’s call this angle \( \theta \). The tangent of \( \theta \) can be expressed as follows:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{4} = \frac{1}{2} \]

To find the angle, we can take the arctangent (inverse tangent) of \( \frac{1}{2} \):

\[ \theta = \tan^{-1}\left(\frac{1}{2}\right) \]

Calculating this using a calculator:

\[ \theta \approx 26.57^\circ \]

Rounding to the nearest whole degree, we have:

\[ \theta \approx 27^\circ \]

Therefore, the approximate angle measure of the angle formed at the top of the triangle logo is 27 degrees.