Find Measure of Angle N in Right Triangle with Legs 7 and 15

Question

Use the diagram (right triangle MPN with right angle at P, PN=15, MP=7) to find $m\angle N$. Round your answer to the nearest tenth.

Accepted Answer

25.0°

Answer

Step 1: Option 1: Use the angle sum property of triangles: the sum of angles in a triangle is 180°. We know the right angle is 90° and $\angle M \approx 65.0°$, so $\angle N = 180° - 90° - 65.0° = 25.0°$. Step 2: Option 2: Use the tangent function: relative to $\angle N$, opposite side = MP=7, adjacent side = PN=15. $\tan(\angle N) = \frac{7}{15}$, so $\angle N = \tan^{-1}(\frac{7}{15}) \approx 25.0°$.