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Using Right Triangle Trigonometry (trig, for short!)

Using Right Triangle Trigonometry (trig, for short!). MathScience Innovation Center Betsey Davis. Geometry SOL 7. The student will solve practical problems using: Pythagorean Theorem Properties of Special Triangles Right Triangle Trigonometry. Practical Problem Example 1.

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Using Right Triangle Trigonometry (trig, for short!)

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  1. Using Right TriangleTrigonometry(trig, for short!) MathScience Innovation Center Betsey Davis

  2. 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

  3. 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? Pythagorean Theorem2^2 +5 ^2 = ? 29 So shortcut is R J Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

  4. 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 30-60-90 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

  5. 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 50 x 100o 30o Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

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

  7. 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

  8. What answers did you get? These ratios are the ratios of the legs and hypotenuse in the right triangle. • Sin 30 = .5 • Cos 30 = .866 • Tan 30 = .577 tan 30 = O/A = 4/6.93=.577 cos 30 = A/H = 6.93/8=.866 Sin 30 = O/H = 4/8=.5 30 8 ? 60 4 ? Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

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

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

  11. Let’s solve for x and y Sin 20 = x /50 cos 20 = y/50 .342 = x/50 17.1 = x 50 x .940 = y/50 47 = y 20o y Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

  12. Do the answers seem reasonable? No, but the diagram is not reasonable either. 50 17.1 20o 47 Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

  13. Practical Problem Example 4 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? Pythagorean Theorem does not work without more sides. It is not a “special” triangle. We must use trig ! 20o 50 feet Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

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

  15. 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. 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? 3 feet Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

  16. Practical Problem Example 5 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? Sin 8.33 = 3/y .145 = 3/y .145y= 3 Y= 3/.145 Y=20.7 feet 3 feet 8.33 o Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

  17. Practical Problem Example 5 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? tan 8.33 = 3/x .146 = 3/x .146x= 3 x= 3/.146 x=20.5 feet 3 feet 8.33 o Using Right Triangle Trig 2005 MathScience Innovation Center B. Davis

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