QuestionFind $\tan B$ given $a=5$ , $b=12$ , and $c=13$ . Also, $\sin B=\frac{12}{13}$ , $\cos B=\frac{5}{13}$ .

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. . The sides of the triangle are a=5, b=12, and c=13.
3. The angle B is the angle opposite side b.
4. The sine of angle B is given by $\sin B = \frac{b}{c}$ .
5. The cosine of angle B is given by $\cos B = \frac{a}{c}$ .
6. The tangent of angle B is given by $\tan B = \frac{b}{a}$ .

STEP 2

We have already been given the sine and cosine of angle B. We need to calculate the tangent of angle B.The formula for the tangent of an angle in a right triangle is $\tan B = \frac{b}{a}$

STEP 3

Now, plug in the given values for sides a and b to calculate the tangent of angle B.
$\tan B = \frac{12}{5}$

STEP 4

implify the expression to get the value of $\tan B$ .
$\tan B = \frac{12}{} =2.4$ The tangent of angle B is2.4.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms