To solve a right-angled triangle means, to find the values of remaining angles and remaining sides under two conditions, namely, when one side and one acute angle are given or when two sides of the triangle are given. There are several ways to determine the missing information in a right triangle. One of these ways is the Pythagorean Theorem, which states that a2+b2=c2.
Suppose you have a right triangle in which a and b are the lengths of the legs, and c is the length of the hypotenuse, as shown below. If you know the length of any two sides, then you can use the Pythagorean Theorem to find the length of the third side. Once you know all the side lengths, you can compute all of the trigonometric functions.
Determining all of the side lengths and angle measures of a right triangle is known as solving a right triangle. Let’s look at how to do this when you’re given one side length and one acute angle measure. Once you learn how to solve a right triangle, you’ll be able to solve many real-world applications – such as the ramp problem at the beginning of this lesson – and the only tools you’ll need are the definitions of the trigonometric functions, the Pythagorean Theorem.