Warm Up Find the missing sides of the following triangles: 3 7 15 8 Can’t do 4th 8

Answers Find the missing sides of the following triangles: 3 7 17 15 Can’t do 4th 7.62 8

Right Triangle Trigonometry

Trigonometry Trigonometry was developed by Greek mathematicians over 2000 years ago. It was created to study astronomy. By understanding the relationships between sides and angles, astronomers could map the movements of planets and stars.

First, we will focus on right triangles! Today, you will learn how to: solve for a missing side of a right triangle solve for a missing angle of a right triangle Later in the unit, we will work with non-right triangles.

Labeling Triangles for Trig First, put stickman next to angle, then you always have hyp across from 90, and adj, opp

You try… Have students come to board and label sides. REMIND STUDENTS OF RATIOS. ONE THING OVER ANOTHER. BOYS TO GIRLS, ETC.

Sine of ∠Ө Define opp/hyp as sine Ө

Cosine of ∠ Ө Define adj/hyp as cosine Ө

Tangent of ∠ Ө Define the ratio “opp/adj” as “Tangent” ∠ Ө

soh cah toa

soh cah toa cos A = cos C = tan A = tan C = Write the 3 Trig Functions for each angle. (A and C) We never use the 90o angle! sin A = sin C = cos A = cos C = tan A = tan C = SIN a, COS a, tan a……sin c, cos c, tan c

Example 2: Finding a Side Length Use a Trig Function and solve using Algebra! Find x. When you need to use your calculator, ALWAYS make sure it’s in DEGREE mode Draw stick figure, what sides do I know? Hyp and opp. So use soh=sin. Sin35=opp/hyp=x/20. now use algebra. CROSS MULTIPLY!!! 20*SIN35=x*1. use calculator in degree mode

Example 3: Finding a Side Length Use trig to solve for x. Stick man. Sides? Adj and hyp. Use cah=cos. Cos72/1=adj/hyp=6/x. cross multiply. xcos73=6. x=6/cos72

Example 4: Working backwards Find the measure of angle C.

Now our three trig functions can be used to find the 
measure of an angle!

Example 6: Find Angle M.

Am I finding an angle or a side? Sine, cosine or tangent? Use the inverse function. Side Sine, cosine, or tangent? Use algebra to solve for the missing side.

Example 1: Hot Air Balloon As a hot-air balloon began to rise, the ground crew drove 1.2 mi to an observation station. The initial observation from the station estimated the angle between the ground and the line of sight to the balloon to be 30º. Approximately how high was the balloon at that point? ‘

The balloon is approximately 0.7 mi, or 3696 ft, high.

Example 2: Width of a River A surveyor can measure the width of a river by standing on point C and taking a sighting at point A on the other side. After turning 90° and walking 200m, he takes another sighting from point B. Angle B is measured and found to be 20°. What is the width of the river? The width of the river is approximately 73 meters.

Example 3: Painting a House For safety reasons, the base of a 25 ft must be 6.5 ft from the base of wall. At what angle with the ground should a painter place his ladder in order to maximize his height? Thus when the ladder is in its safest position, it makes an angle of about 75º with the ground.