Unit 2

Unit 5: Trigonometry Final Exam Review

Topics to IncludePythagorean TheoremTrigonometryFind a Missing Side LengthFind a Missing Angle MeasureAngle of Elevation and DepressionArea of a Triangle (SAS)Area of a Triangle (SSS)Pythagorean TheoremThe Pythagorean Theorem is used to find MISSING SIDE LENGTHS in RIGHT triangles.The theorem: a2 + b2 = c2a and b are the LEGSc must be the HYPOTENUSEPythagorean Theorem

Pythagorean TheoremNow you try:

Pythagorean TheoremYou can also use the Pythagorean Theorem to determine if a triangle is a RIGHT triangleIf you perform the Pythagorean Theorem and the equation is EQUAL, then the triangle IS a right triangleIf you perform the Pythagorean Theorem and the equation is NOT EQUAL, then the triangle is NOT a right trianglePythagorean TheoremExampleA = 4, B = 10, C = 12

a2 + b2 = c242 + 102 = 12216 + 100 = 144116 = 144NO, the triangle is not a right triangle

Pythagorean TheoremNow you try: A = 9, B = 40, C = 41 TrigonometryTrigonometry is used in order to find missing SIDE LENGTHS and missing ANGLE MEASURES in a right triangleThere are 3 trigonometric ratiosSINECOSINETANGENTIn order to correctly find the missing side or angle, you must use the CORRECT ratioTrigonometrySOHCAHTOASineOPPOSITE over HYPOTENUSECosineADJACENT over HYPOTENUSETangentOPPOSITE over ADJACENT

TrigonometryExampleWhich trig ratio would you use?

You would use TANGENTYou would use SINE

Finding a Missing Side LengthTo find a missing side length: Determine which RATIO to use (sine, cosine, or tangent)Set up the problem using the given ANGLE measurePut a 1 under the trig ratioCROSS multiplyMake sure your calculator is in DEGREE MODEFind a Missing Side LengthWatch this video for an example on how to find a missing side length

Find a Missing Side LengthNow try this:

Finding a Missing Angle MeasureTo find a missing angle measure: Determine which RATIO to use (sine, cosine, or tangent)Set up the problem using the given ANGLE measureUse the INVERSE trig button in your calculatorMake sure your calculator is in DEGREE MODE

Find a Missing Angle measureWatch this video for an example on how to find a missing angle measure

Finding a Missing Angle MeasureNow you try:

1. 2.

Angle of Elevation and DepressionAngles of Elevation and Depression are used in WORD PROBLEMS in order to find missing angles and side lengths

Angle of ElevationAngle of Depression

The Angle of Elevation and the Angle of Depression are ALWAYS EQUAL

Angle of Elevation and DepressionNow you try:An escalator from the ground floor to the second floor of a department store is 110 ft long and rises 32 ft. vertically. What is the escalators angle of elevation? From the top of a lighthouse 210 feet high, the angle of depression of a boat is 27. Find the distance from the boat to the foot of the lighthouse. The lighthouse was built at sea level.

Area of a Triangle (SAS)

Area of a Triangle (SAS)Try this one:

Find the area of the triangle

Area of a Triangle (SSS)

Area of a Triangle (SSS)Now try this:

Find the area of the triangle

ALL DONE