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 answer

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

In this case, the height of the triangle (which is opposite the angle we want to find) is 2 inches, and the base (which is adjacent to the angle) is 4 inches.

We can denote the angle at the top of the triangle as \( \theta \). The tangent of angle \( \theta \) is given by:

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

Now, to find the angle \( \theta \), we can use the arctangent function (inverse tangent):

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

Using a calculator, we can find:

\[ \theta \approx 26.565^\circ \]

Rounding \( \theta \) to the nearest whole degree gives:

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

Thus, the approximate angle measure of the angle formed at the top of the triangle logo is \( \boxed{27} \) degrees.