Using Right Triangle Trigonometry (trig, for short!) MathScience Innovation Center Betsey Davis

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Geometry SOL 7 The student will solve practical problems using: Pythagorean Theorem Properties of Special Triangles Right Triangle Trigonometry

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 1 Jenny lives 2 blocks down and 5 blocks over from Roger. How far will Jenny need to walk if she takes the short cut? J R Pythagorean Theorem 2^2 +5 ^2 = ? 29 So shortcut is

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 2 Shawna wants to build a triangular deck to fit in the back corner of her house. How many feet of railing will she need across the opening? Special triangle Hypotenuse is 10 feet She will need 10 feet of railing 5 feet Railing across here

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 3 Rianna wants to find the angle between her closet and bed. We don’t need the pythagorean theorem It is not a special triangle We don’t need trig We just need to know the 3 angles add up to 180 X is o x 30 o

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Review Find: Sin A Cos A Tan A A = 5/13 = 12/13 = 5/12 S = O/H C = A/H T = O/A

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis If you know the angles, the calculator gives you sin, cos, or tan: Check MODE to be sure DEGREE is highlighted (not radian) Press SIN 30 ENTER Press COS 30 ENTER Press TAN 30 ENTER Write down your 3 answers

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis What answers did you get? Sin 30 =.5 Cos 30 =.866 Tan 30 =.577 These ratios are the ratios of the legs and hypotenuse in the right triangle ? ? 4 Sin 30 = O/H = 4/8=.5cos 30 = A/H = 6.93/8=.866tan 30 = O/A = 4/6.93=.577

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis If sin, cos, tan can be found on the calculator, we can use them to find missing triangle sides. 20 o 50 ? ?

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis If sin, cos, tan can be found on the calculator, we can use them to find missing triangle sides. 20 o 50 x y Sin 20 = x /50 Cos 20 = y/50 Tan 20 = x /y

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Let’s solve for x and y 20 o 50 x y Sin 20 = x /50 cos 20 = y/ = x/ = x.940 = y/50 47 = y

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Do the answers seem reasonable? 20 o No, but the diagram is not reasonable either.

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 4 Pythagorean Theorem does not work without more sides. It is not a “special” triangle. We must use trig ! 50 feet 20 o Jared wants to know the height of the flagpole. He measures 50 feet away from the base of the pole and can see the top at a 20 degree angle. How tall is the pole?

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 4 Which of the 3 choices: sin, cos, tan uses the 50 and the x???? 50 feet 20 o Tan 20 = x/50 Press tan 20 enter So now we know.364 = x/50 Multiply both sides by 50 X = 18.2 feet

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 5 Federal Laws specify that the ramp angle used for a wheelchair ramp must be less than or equal to 8.33 degrees. 3 feet You want to build a ramp to go up 3 feet into a house. What horizontal space will you need? How long must the ramp be?

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 5 3 feet You want to build a ramp to go up 3 feet into a house. What horizontal space will you need? How long must the ramp be? 8.33 o Sin 8.33 = 3/y.145 = 3/y.145y= 3 Y= 3/.145 Y=20.7 feet

Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis Practical Problem Example 5 3 feet You want to build a ramp to go up 3 feet into a house. What horizontal space will you need? How long must the ramp be? 8.33 o tan 8.33 = 3/x.146 = 3/x.146x= 3 x= 3/.146 x=20.5 feet