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 ?
To find the angle measure at vertex N, we can use the inverse trigonometric function sine.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we want to find the sine of angle N.
sin(N) = opposite/hypotenuse
sin(N) = LM/MN
sin(N) = 8/10
sin(N) = 0.8
To find the angle itself, we can use the inverse sine function (also known as arcsine) on a calculator.
N = sin^(-1)(0.8)
N ≈ 53.13 degrees
Therefore, the approximate angle measure at vertex N is 53.13 degrees.