Right triangle LMN is drawn on paper. The right angle is located at vertex L with side length MN as the hypotenuse. The side length measurements are LM=8 units , MN=10 units , and NL=6 units . What is the approximate angle measure at vertex N ?(1 point) Responses 39° 39° 37° 37° 53° 53° 31°
To find the angle measure at vertex N, we can use the trigonometric function sine.
We know that the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the angle at vertex N is LM, which has a length of 8 units, and the hypotenuse is MN, which has a length of 10 units.
So, sin(N) = LM/MN = 8/10 = 4/5.
To find the angle N, we can take the inverse sine of 4/5 using a calculator.
Approximating to the nearest degree, the angle N is 53°.