Geometry Chapter 7 - Right Triangles and Trigonometry Section 7.5-7.6 - Apply the Sin, Cos, and Tan ratios

What the student should get from this: 1. Find the sin, cos, and tan of an acute angle 2. Use trig ratios to find side lengths in right triangles and to solve real-world problems Let’s look at some new stuff... on your calculator, find the sin, cos, and tan buttons. These are trig ratios. Sin, cos, and tan are all ratios. The sine of an angle in a right triangle is the ratio of the opposite side over the hypotenuse. sin A =

B

sin B = c a

The cosine of an angle in a right triangle is the ratio of the adjacent side over the hypotenuse. cos A =

C

cos B =

The tangent of an angle in a right triangle is the ratio of the opposite side over the adjacent side. tan A =

tan B =

Example 1: sin A =

B

sin B = 5

13

cos A = cos B =

C

12

A

tan A = tan B =

b

A

Example 2: Let’s do a little calculator practice. sin 32˚ =

cos 46˚ =

tan 45˚ =

sin 81˚ =

cos 38˚ =

tan 83˚ =

sin 16˚ =

cos 2˚ =

tan 27˚ =

Example 3: Find x and y in each of the following triangle:

58˚ y

y

x

8 in. 26˚ 6 in.

x

y 18˚ y x

x 4 ft

32˚ 12 cm

Example 4: Find the area of the triangles. w 18˚

y x

x 4 ft

31˚ 7 in.

Example 5: Find the perimeter of the triangles.

w 22˚

52˚

y 15 ft

x

x

9 in.

Example 6: Solve for the measure of C

21

and B

in each triangle. A 16

15

A

11.5

C

Show work to get credit. Assignment: p.470 #s 19-22, 25-29 all and p.477 #s 8-11 all, 16, 21-24 all - due next class. One class period late will be 50% off. Beyond that, no credit given. Study for the Daily Quiz

B