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CCGPS Geometry Day 17 ( ) UNIT QUESTION: What patterns can I find in right triangles? Standard: MCC9-12.G.SRT.6-8 Today’s Question: How do we use trig ratios to find the missing sides and angles of a triangle? Standard: MCC9-12.G.SRT.6-8

opposite hypotenuse adjacent hypotenuse opposite adjacent

Finding an angle. (Figuring out which ratio to use and getting to use an inverse trig button.)

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m 40 m Tan / 40 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 15 m 50 m Sin / 50 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex. 3: Find . Round to the nearest degree

Ex. 4: Find . Round to the nearest degree. 23 7

Ex. 5: Find . Round to the nearest degree

Finding a side. (Figuring out which ratio to use and getting to use a trig button.)

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m x tan 2055 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 2 Find the missing side. Round to the nearest tenth. 80 ft x tan 8072 =  ( ) ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 3 Find the missing side. Round to the nearest tenth. 283 m x Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft x

When we are trying to find a side we use sin, cos, or tan. When we are trying to find an angle we use ( INVERSE ) sin -1, cos -1, or tan -1.