Test grades will be in Wed afternoon Test corrections Thu, Fri, Mon am and pm Retakes Thu, Fri, Mon pm ONLY Pick up trig packet

10/2 Test grades were posted Wed afternoon Test corrections Thu, Fri, Mon am and pm Retakes Thu, Fri, Mon pm ONLY. End of six weeks is Friday Yesterday we reviewed trig. The notes are on line. We began the trig packet Today you will complete trig packet. It is due at the EOC. Pay attention to units: all sides must match! 1inch = 2.54 cm

What does it mean to say “as the crow flies”?

What is the Pythagorean Theorem? c 2 = a 2 + b 2

Side labels

L K J Name the sides

L adj K opp J hyp Name the sides

SOH CAH TOA

What does Sin θ stand for? Ratio of Opposite / Hypotenuse for a given angle What does Cos θ stand for? Ratio of Adjacent / Hypotenuse for a given angle What does Tan θ stand for? Ratio of Opposite / Adjacent for a given angle

CosSinCotSecCscTanDegRad

Find the tan for the given angle First name the sides Tan = Opp/Adj = 11.2 cm/8.4 cm = cm 11.2 cm 14 cm

Use tan function to fin the tan (ie. The ratio) Tan (53.13º) Tan (53.13º) = 1.333

Use inverse tan function to find the angle if Tan θ = Tan -1 (1.333) = 53.12º

We have looked at: Pythagoreans Naming sides Determining ratios Determining sides Determining angles

Summary Ratios: sin θ, cos θ and tan θ describe ratio of two sides. No unit. Can determine two ways(ex with sin): –Knowing the angle: sin(30º) = 0.5 –Knowing the sides: sin θ= Opp/Hyp sin θ =5m/10m =.5 5m 10m 30º

Summary Angles: To find angles use the inverse of the appropiate function:sin -1, cos -1 and tan -1 Can determine two ways(ex with sin): –Knowing the sides: sin -1 (5m/10m)= 30º –Knowing the ratio: sin -1 (.5)= 30º 5m 10m 30º

Summary Putting it all together: If you need to determine a side: Name sides in reference to known angle Determine formula You know angle and hypotenuse, want opposite: Opp = (sin θ)(Hyp) (sin30º)(10m) = 5m ?? opp 10m hyp 30º

Summary Putting it all together: If you need to determine an angle : Name sides in reference to angle of interest Determine formula –You know opp and hypotenuse, want θ : sin -1 = (Opp/ Hyp) –sin -1 (5m/10m)=30º 5m opp 10m hyp Θ ??

1. 32 m 55º = m = m a = m b = m Sin 55° = a b B 32 m B = (32 m)(sin 55°) To solve for a…

Find R and Ө. 2.

Finding a side The Church Steeple Eric decides to find the height of the steeple of his local church. He measures a distance of 50. m along the ground. The angle of elevation of the top of the steeple is 35°in reference to the ground. How high is the steeple? Step 1. Draw a diagram. 50.m 35° ?

The Church Steeple ? 50m 35° Have the Adjacent side and an angle Want the Opposite side. Use tan  = opp/adj Opp = (tan  adj) Opposite= (tan 35°)(50m) = 35 m

Finding An Angle The Airplane At Bush IAH airport there is a forest just 500. m from the end of the runway. The trees can be as tall as 30. m. What is the minimum angle of climb if aircraft are to avoid the trees? Step 1. Draw a diagram. 30.m 500.m ?

Finding An Angle  Have the Adjacent and Opposite sides Want the angle Use tan  = opp/adj To find angles need to use tan  -1  tan  -1 (30m/500m)  = 3.4º