How to find an angle with tangent

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ACT Math › How to find an angle with tangent

Questions 1 - 5
1

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?

Explanation

You can draw your scenario using the following right triangle:

Theta5

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 .

2

Soh_cah_toa

For the above triangle, and . Find .

This triangle cannot exist.

Explanation

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.

3

Soh_cah_toa

For the above triangle, and . Find .

This triangle cannot exist.

Explanation

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.

4

Soh_cah_toa

In the above triangle, and . Find .

Explanation

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.

5

Theta4

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

Explanation

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 .

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