9.5 Trigonometric ratios How are trigonometric ratios used to find missing sides of right triangles?

Trig ratio- ratio of the lengths of two sides of a right Δ. Used to find missing side lengths when only 1 length is known. Always round to four decimal places 38° 12

3 basic trig ratios Sine (sin) Cosine (cos) Tangent (tan) Sin  Cos  Tan 

Just remember Chief… SOH CAH TOA ineine ppositepposite ypotenusypotenus osineosine djacentdjacent ypotenusypotenus angentangent ppositepposite djacentdjacent

Ratios of  s A and B AA BB A B C a b c

Ex: Find sin, cos, & tan of  A &  B. AA sin A= 12/13 =.9231 cos A= 5/13 =.3846 tan A= 12/5 = 2.4 BB sin B= 5/13 =.3846 cos B= 12/13 =.9231 tan B= 5/12 =.4167 C A B

Example __ 1 2 A B C sin A= ½ or.5 sin 30=.5 Find sin A and sin 30 o.

Example 45 __ A B C 1 1 sin 45 o =.7071 Find sin B and sin 45 o.

Using your calculator find tan 23 sin 72 cos 44

Assignment Trigonometric Ratios WS #1-24

Use trig to solve for n.

Use trig to solve for m.

Use trig to find t.

Use trig to find z.

Angle of elevation  ground angle of elevation

Example Find the height of the tree 48 o 100 ft __ h You are given the adj side & finding the opp side. Use tangent!! tan 48 o = h/ = h About 111 ft 100 tan 48 o = h

Example 100ft 30 o d __ Have opp side need hypot Use sine!!.5d=1000 d=2000 ft

Assignment Assignment Trigonometry WS #1-18 Assignment