1. The measure of angle L is 70°.
2. The trigonometric ratio that uses ∠M and LN to solve for NM is tangent.
3. The length of NM, to the nearest tenth, is approximately 57.7.
What is the measure of angle L?
1.
The measure of angle L:
Angle L + Angle M + Angle N = 180° (sum of angles in a triangle)
Angle L + 20° + 90° = 180°
Angle L + 110° = 180°
Angle L = 180° - 110°
Angle L = 70°
2.
The trigonometric ratio that uses ∠M and LN to solve for NM is tangent
3.
tan 20° = opposite / adjacent
tan 20° = 21/x
tan 20° × x = 21
x = 21/tan 20°
x = 57.69702580854706
Approximately,
x = 57.7
Therefore, length of NM, to the nearest tenth, is approximately 57.7