To solve for the missing angle B, we used the given information of the sine of angle LB and the lengths of two sides. By taking the inverse sine of the ratio, we found that angle B is approximately 75.036 degrees.
To solve for the missing angle, we can use the trigonometric ratio of sine. The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this problem, we are given the lengths of two sides and the sine of one angle. Let's label the missing angle as angle B and the given angle as angle LB.
From the given information, we have:
sin(LB) = 71/24
sin(B) = unknown/16
To solve for angle B, we can use the property of inverse sine (also known as arcsine). Taking the inverse sine of both sides of the equation, we get:
B = sin^(-1)(unknown/16)
Now, we can substitute the value of sin(LB) into the equation:
B = sin^(-1)(71/24/16)
Using a calculator set to degrees, we can evaluate the expression:
B ≈ 75.036
Therefore, the missing angle B is approximately 75.036 degrees.