QuestionFind side $c$ with $a=5$ , $b=12$ . Then calculate $\sin B$ and simplify the results.

Studdy Solution

STEP 1

Assumptions1. We are given a right triangle with sides a, b, and c. . The lengths of sides a and b are given as5 and12 respectively.
3. The length of side c is given as13.
4. We are asked to find the value of $\sin B$ , where B is one of the angles of the triangle.

STEP 2

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 our case, we are looking for $\sin B$ , where B is the angle opposite to side b.
$\sin B = \frac{b}{c}$

STEP 3

Now, plug in the given values for side b and side c to calculate $\sin B$ .
$\sin B = \frac{12}{13}$

STEP 4

implify the fraction to get the value of $\sin B$ .
$\sin B = \frac{12}{13}$ So, $\sin B = \frac{12}{13}$ .

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