The legs of a right triangle are 5 and 6 units long. Find the measure of the second largest angle of the triangle. Round your answer to the nearest tenth. Please explain?

Jun 4, 2018

In a right triangle the largest angle is ${90}^{\circ}$ and the middle angle is opposite the long leg, here $\arctan \left(\frac{6}{5}\right) .$

Jun 4, 2018

The second largest angle = ${\tan}^{-} 1 1.2 \approx {50.2}^{o}$

Explanation:

The triangle in question looks like this:

As AB on the figure is longer than AC, $\angle C$ is the second largest angle (the right angle $\angle A$ being the largest of course).
We have $\tan \angle C = A \frac{B}{A} C = \frac{6}{5} = 1.2$
Therefore $\angle C = \arctan 1.2 \approx {50.2}^{o}$
(another notation for arctan is ${\tan}^{-} 1$)