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?

2 Answers
Dean R.
Jun 4, 2018

In a right triangle the largest angle is #90^circ# and the middle angle is opposite the long leg, here #arctan (6/5).#

Roy Ø.
Jun 4, 2018

The second largest angle = #tan^-1 1.2~~50.2^o#

Explanation:

The triangle in question looks like this:
enter image source here
As AB on the figure is longer than AC, #/_C# is the second largest angle (the right angle #/_A# being the largest of course).
We have #tan /_C=AB/AC=6/5=1.2#
Therefore #/_C= arctan1.2~~50.2^o#
(another notation for arctan is #tan^-1#)

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