13.1 Right Triangle Trigonometry Objectives: Find values of trig function for acute angles. Solve problems involving right triangles.

Trigonometry Trigonometry is the study of the relationships among the angles and sides of a right triangle. There are 6 trig ratios that relate the sides and acute angles of a right triangle – sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). sine and cosecant; cosine and secant; and tangent and cotangent have reciprocal relationships.

Trig Functions If θ (Greek letter theta) is the measure of an acute angle of a right triangle, opp is the measure of the leg opposite θ, adj is the measure of the leg adjacent to θ, and hyp is the measure of the hypotenuse, then the following are true. hyp opp θ adj

Other relationships Since sin and csc, cos and sec, and tan and cot are reciprocals, the following is true:

Finding Trig ratios Use the triangle to find the 6 trig functions for angle θ. θ 5 13 12

Finding other ratios from one. 5 Use the ratio to find the sin ratio. 3 A

Special Right Triangles

Finding missing sides Use the triangle to find the missing side. Using trig: Using 30-60-90 Shorter leg=6, longer leg=

Finding missing angles Use the triangle to find the missing angle.

Solving a right triangle To solve a right triangle, find any missing angle(s) or side(s). You must have at least 2 pieces of information. One of these must be a side. Use the easiest way to find the missing parts – Pythagorean Theorem, 180° in a triangle.

Solve ΔABC Round sides to the nearest tenth, angles to the nearest degree. Need to find: c, a, B B=62

Application Problems Trig can be used to find distances or lengths that cannot be measured directly. Angle of elevation – the angle between a horizontal line and the line of sight from the observer to an object at a higher level Angle of depression – the angle between a horizontal line and the line of sight from the observer to an object at a lower level. Angle of depression→ ←Angle of elevation

Example A ski run has an angle of elevation of 15.7° and a vertical drop of 1800 feet. Estimate the length of this run. Use trig to find missing part.

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