Question

a triangle has angle measures of 40°, 59°, and 81°. the side opposite the 40° angle is 11 centimeters long. find the length of the side opposite the 81° angle to the nearest centimeter

Answer 1

We can use the Law of Sines to solve this, which states that $\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}$. We can name the triangle like the one below to see that $\frac{11}{sin40} = \frac{b}{sin81}$. We move the 11 up to sin81 to get that $\frac{11sin81}{sin40}$, which simplifies to 17 (rounded).

:)