Right Triangle Trigonometry Trigonometry is based upon ratios of the sides of right triangles. The ratio of sides in triangles with the same angles is consistent. The size of the triangle does not matter because the triangles are similar (same shape different size). 1

2 The six trigonometric functions of a right triangle, with an acute angle , are defined by ratios of two sides of the triangle. The sides of the right triangle are:  the side opposite the acute angle ,  the side adjacent to the acute angle ,  and the hypotenuse of the right triangle. opp adj hyp θ

3 The trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. opp adj hyp θ Trigonometric Functions sin  = cos  = tan  = csc  = sec  = cot  = opp hyp adj hyp adj opp adj Note: sine and cosecant are reciprocals, cosine and secant are reciprocals, and tangent and cotangent are reciprocals.

4 Reciprocal Functions Another way to look at it… sin  = 1/csc  csc  = 1/sin  cos  = 1/sec  sec  = 1/cos  tan  = 1/cot  cot  = 1/tan 

Given 2 sides of a right triangle you should be able to find the value of all 6 trigonometric functions. Example: 

Standard Triangle with A, B, C, a, b, and c Angles: capital letters (A, B, and C) or greek letters (θ, α) Sides: lower case letters (a, b, c) Same letters are opposite of each other. A b c C B a

Solve for all missing sides and angles if b = 5 and c = 10. Assume C is the right angle. 1 st : Draw the triangle 2 nd :Pick an angle to use as a reference 3 rd : Label opposite, adjacent, and hypotenuse 4 th : Start solving!

You are 330 feet from the base of a building. The angles of elevation to the top and bottom of a flagpole on top of the building are 55 o and 53 o. Find the height of the flag pole. 1 st : Draw the picture 2 nd : Solve for each triangle 3 rd : Answer the question

Exit slip time! Homework: Day 3 on assignment guide! (I have the dates wrong!) Quiz coming up on Friday (this is a change from the assignment guide)