# ACT Math : How to find the tangent of an angle

## Example Questions

### Example Question #1 : Trigonometry

What is the tangent of C in the given right triangle??

Explanation:

### Example Question #1 : How To Find The Tangent Of An Angle

Consider a right triangle with an inner angle .

If

and

what is ?

Explanation:

The tangent of an angle x is defined as

Substituting the given values for cos x and sin x, we get

### Example Question #2 : How To Find The Tangent Of An Angle

Triangle ABC shown is a right triangle. If the tangent of angle C is , what is the length of segment BC?

Explanation:

Use the definition of the tangent and plug in the values given:

tangent C = Opposite / Adjacent = AB / BC = 3 / 7

Therefore, BC = 7.

### Example Question #3 : How To Find The Tangent Of An Angle

If the sine of an angle equals , and the cosine of the same angle equals , what is the tangent of the angle?

Explanation:

The cosine of the angle is  and since that is a reduced fraction, we know the hypotenuse is  and the adjacent side equals .

The sine of the angle equals , and since the hyptenuse is already  we know that we must multiply the numerator and denominator by  to get the common denominator of .  Therefore, the opposite side equals .