Algebra and Trigonometry, 5th Edition

6.2 Applications of Right Triangles

• Solve right triangles.

• Solve applied problems involving right triangles and trigonometric functions.

Solving Right Triangles

Now that we can find function values for any acute angle, it is possible to solve right triangles. To solve a triangle means to find the lengths of all sides and the measures of all angles.

Example 1

In $\mathrm{\Delta }\mathit{ABC}$ (shown at left), find a, b, and B, where a and b represent lengths of sides and B represents the measure of $\angle B$. Here we use standard lettering for naming the sides and the angles of a right triangle: Side a is opposite angle A, side b is opposite angle B, where a and b are the legs, and side c, the hypotenuse, is opposite angle C, the right angle.

Solution

In $\mathrm{\Delta }ABC$, we ...