Algebra 2 cc Section 7.1 Solve right triangles “Trigonometry” means triangle measurement and is used to solve problems involving triangle. The sides of a right triangle are named based on the position of an acute angle.

The three sides of a right triangle can be grouped into six different ratios. Each ratio has its own name. SOH – CAH - TOA Trigonometric Ratio Sine sin θ= opposite hypotenuse Cosinecos θ= adjacent hypotenuse Tangenttan θ= opposite adjacent

Other trigonometric ratios Cosecantcsc θ= hypotenuse opposite Secantsec θ= hypotenuse adjacent Cotangentcot θ= adjacent opposite Reciprocal Relationships sin θ= 1 csc θ= 1 csc θsin θ cos θ=1 sec θ= 1 sec θ cos θ tan θ= 1cot θ= 1 cot θ tan θ

Evaluate the six trigonometric functions of the angle θ shown in the right triangle.

Find the sin θ for each triangle. The value of a trigonometric function depends only upon the angle and not upon the size of the triangle.

Use a calculator to evaluate the following trigonometric functions. sin 23 o cos 56 o tan 81 o sec 13 o csc 52 o cot 46 o

Solve the triangle. (Find the missing sides and angles.)

Cah ties a zip line to the top of the tree to slide down quicker. The angle of elevation to the top of the tree from a point 120 ft from the base of the tree is 35 degrees. How tall is the tree?

It is possible to determine the value of some trigonometric functions based on special triangles. Evaluate without a calculator. sin 30 o = _____ cos 30 o = _____ tan 60 o = _____ sec 60 o = _____ tan 45 o = _____ cot 45 o = _____ sin 45 o = _____ csc 60 o = _____

assignment Page 772 Problems 16 – 24 even, 25 – 32 all, even, all