TRIGONOMETRY Lesson 2: Solving Right Triangles

Todays Objectives Students will be able to develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles, including: Solve right triangles, with or without technology

Using Trigonometry to solve for a side In order to find an unknown side measure in a right triangle using trig ratios, the length of one other side and the measure of one of the acute angles is required. Example: Solve for the side length x to the nearest tenth of a centimeter Solution: First, identify the positions of the side lengths relative to the acute angle whose measure is known Since the length of the hypotenuse and opposite side is required (side x), the opposite-hypotenuse ratio is used. This is the sine ratio 10 cm 62° x hypotenuse adjacent opposite

Example 46 m x 37°

Example A B C 55° 50 in. x

Using Trigonometry to Solve for an Angle 15 cm 6 cm

Example hypotenuse opposite adjacent

Example: 30 m 40 m

Solving Triangles Often, you will need to determine all the unknown measures of the sides and angles of a triangle. This is referred to as solving the triangle. In order to solve a triangle, it is common to use one or more of the following: Pythagorean theorem Sum of angles in a triangle Trigonometric ratios

Example 12 cm y x35°

Example

Example: Solve the following triangle. Give the unknown side length to the nearest tenth of a centimeter, and give unknown angles to the nearest tenth of a degree. Solution: Side AC = 6 cm, Angle A = 53.1°, Angle B = 36.9° C B A 8 cm 10 cm