### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find An Angle With Tangent

For the above triangle, and . Find .

**Possible Answers:**

This triangle cannot exist.

**Correct answer:**

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

### Example Question #1 : Trigonometry

In the above triangle, and . Find .

**Possible Answers:**

**Correct answer:**

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

### Example Question #1 : How To Find An Angle With Tangent

For the above triangle, and . Find .

**Possible Answers:**

This triangle cannot exist.

**Correct answer:**

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

### Example Question #4 : How To Find An Angle With Tangent

A laser is placed at a distance of from the base of a building that is tall. What is the angle of the laser (presuming that it is at ground level) in order that it point at the top of the building?

**Possible Answers:**

**Correct answer:**

You can draw your scenario using the following right triangle:

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

or .

### Example Question #5 : How To Find An Angle With Tangent

What is the value of in the right triangle above? Round to the nearest hundredth of a degree.

**Possible Answers:**

**Correct answer:**

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

or .