Question

M is a right angle in triangle LMN. The measure of angle Nis 67º and the length of MN is 8.What is the length of the hypotenuse? Round to the nearest tenth.There is no picture provided. Please help me in a timely manner.

Answer 1

We will have the following:

*First: We determine the measure of angle L:

$L+M+N=180\Rightarrow L+90+67=180$$\Rightarrow L=23$

So, the measure of angle L is 23°.

*Second: We will use the measure of MN and the angle of L to determine the length of the hypotenuse:

$8=h\sin (23)\Rightarrow h=\frac{8}{\sin (23)}$$\Rightarrow h=20.47443732\ldots\Rightarrow h\approx20.5$

So, the length of the hypotenus is approximately 20.5 units.

Here is the graph that shows the scenario: