Question

If X = 27 yards, Y = 120 yards, and Z = 123 yards, what is the sine of B?

Answer 1

To find the sine of angle B, calculate the lengths of the sides of triangle XYZ and use the sine function.

Step-by-step explanation:

The sine of angle B can be found using the given values of X, Y, and Z.

First, we need to find the lengths of the sides of triangle XYZ. Using the Pythagorean theorem, we can calculate:

XY = sqrt(X^2 + Y^2) = sqrt(27^2 + 120^2) = sqrt(729 + 14400) = sqrt(15129) = 123

Now, we can use the sine function to find the sine of angle B:

sin(B) = Y/XY = 120/123 ≈ 0.976

Answer 2

Using the Law of Cosines
Renaming sides X, Y and Z
A= 27 yards B = 120 yards, and C = 123 yards, what is the sine of B?
cos (B) = (a^2 + c^2 -b^2) / (2 * a * c)
cos (B) = (27^2 +123^2 -120^2) / (2*27*123)
cos (B) = (729 + 15,129 - 14,400) / 6,642
cos (B) = 1,458 / 6,642
cos (B) = 0.2195121951220
cos (B) = 77.32 degrees