Question

A right triangle has side lengths 5, 12, and 13 as shown below.

Use these lengths to find tanB, sin B, and cos B.

Answer 1

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side, the sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse, and the cosine of an acute angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Using the side lengths given in the problem, we can identify that angle B is the acute angle opposite the side with length 5.

So, we have:

tanB = opposite/adjacent = 12/5

sinB = opposite/hypotenuse = 12/13

cosB = adjacent/hypotenuse = 5/13

Therefore, the values of the trigonometric functions for angle B in this right triangle are:

tanB = 12/5

sinB = 12/13

cosB = 5/13