Question

suppose abc is a right triangle with sides a, b, and c and right angle at c. find the unknown side length using the pythagorean theorem and then find the values of the six trigonometric functions for angle b. a = 3, c = 5 the unknown side length b is 4. (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) sin b = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall sine - function definition

The sine of an angle in a right - triangle is defined as $\sin B=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify opposite and hypotenuse for angle B

For angle $B$ in right - triangle $ABC$, the side opposite to angle $B$ is $b = 4$ and the hypotenuse is $c = 5$.

Step3: Calculate $\sin B$

$\sin B=\frac{b}{c}=\frac{4}{5}$

Answer:

$\frac{4}{5}$