How to Find Angle with Tangent: Solving for Missing Lengths in a Right Triangle

When faced with a right triangle that has an angle and a missing side length, it can be challenging to find the solution. Two common methods to find the missing side of a right triangle include using the Pythagorean theorem or special right triangles. However, what do you do if neither of these methods apply to your problem? This is where trigonometric functions come in handy.

There are three trigonometric functions: sine, cosine, and tangent. To determine which one to use to solve for the missing length, you need to identify which side lengths of the triangle you know. In the example given, the problem provides the adjacent side length and asks to solve for the opposite side length.

Since tangent represents the ratio of the opposite over adjacent, this is the function to use in this problem. To solve for the missing length, you need to plug in the angle and known side length into the tangent function, which gives you a number. Then, you can solve for the missing length using basic algebra.

In the example given, the angle is 25 degrees, and the known side length is 7. To solve for the missing length, labeled as x, you can use the equation x = 7 times the tangent of 25 degrees. Using a scientific calculator to input the equation, you can find that the missing length x is equal to 3.26.

By using trigonometric functions, you can solve for missing lengths in a right triangle when other methods do not apply. Remember to identify the side lengths you know to determine which function to use, and then plug in the angle and known side length to solve for the missing length.


What is the angle from a tangent?
In geometry, the tangential angle of a curve in the Cartesian plane, at a specific point, is the angle between the tangent line to the curve at the given point and the x-axis.