Presentation on theme: " A trigonometric ratio is a ratio of the lengths of 2 sides of a right triangle. You will learn to use trigonometric ratios of a right triangle to determine."— Presentation transcript:
A trigonometric ratio is a ratio of the lengths of 2 sides of a right triangle. You will learn to use trigonometric ratios of a right triangle to determine side length and angle measurement.
Trigonometry is from the ancient Greek language and means “measurement of triangles”, and was first used in 1595. The 3 basic ratios are sine, cosine and tangent. These are abbreviated as sin, cos, and tan respectively.
The sine, cosine, and tangent of the acute angle A are defined as: › A Hypotenuse Side adjacent A Side opposite A
Sketch a 30 -60 -90 triangle. Use “1” as the length of the shorter leg. Therefore the hypotenuse will be 2 and the longer leg will be 1 3. › 30 2 33 1 Note: Similar triangles always have the same trig ratios!!!!
You are measuring the height of a tree. You stand 45 feet from the base of the tree. You measure the angle of elevation from a point on the ground to the top of the tree to be 59 (because you always carry around a clinometer, which allows you to do this). What trig ratio would use the known measures height and elevation? 59 45ft h
Sin M 0.5812 Cos M 0.8137 Tan M 0.7143 Sin T 0.8137 Cos T 0.5812 Tan T 1.4 Sin A 0.7071 Cos A 0.7071 Tan A = 1 Sin N 0.7071 Cos N 0.7071 Tan N = 1 Sin Q = 0.8 Cos Q = 0.6 Tan Q 1.3333 Sin R = 0.6 Cos R = 0.8 Tan R = 0.75
Find the value of each variable. Round decimals to the nearest tenth. 1. 2. x 10.4, y 6.7x 1.7, y 4.7