### All ACT Math Resources

## Example Questions

### Example Question #1 : Trigonometry

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

**Possible Answers:**

**Correct answer:**

Tangent = Opposite / Adjacent

### Example Question #2 : Trigonometry

Consider a right triangle with an inner angle .

If

and

what is ?

**Possible Answers:**

**Correct answer:**

The tangent of an angle *x *is defined as

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

### Example Question #1 : 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?

**Possible Answers:**

**Correct answer:**

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 #2 : 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?

**Possible Answers:**

**Correct answer:**

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 .

Since , the answer is .

Certified Tutor

### All ACT Math Resources

### Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: