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Right Triangles

This test review covers the Pythagorean Theorem, special angles in right triangles, and trigonometry. It includes terminology, steps to solve problems, and practice exercises.

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Right Triangles

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  1. Right Triangles Test Review Pythagorean Theorem, Special angles, and Trig Triangles

  2. Pythagorean Theorem a2 + b2 = c2

  3. Terminology • We call the two sides that touch the right angle the LEGS. They are the a and b. • The side opposite the right angle is the hypotenuse. It is the c. • Label each part.

  4. Terminology • The hypotenuse is always the longest side but shorter than the two legs put together. • Here is the 60 Second Review

  5. Steps to Solve If you know the 2 legs – square the numbers – add- take square root.

  6. Steps to Solve Don’t forget to take the square root. If you know the hypotenuse and one leg – square the numbers - subtract – take the square root.

  7. Special Right Angles 45 – 45- 90

  8. Special Right Angles

  9. Special Right Angles H = hyptonuse L = leg

  10. Special Right Angles

  11. Pythagorean Theorem, Special angles, and Trig Triangles

  12. Special Right Angles 30-60-90 30-60-90

  13. Special Right Angles

  14. Special Right Angles

  15. Short Cut Pattern Formulas

  16. Easy Practice Find x and y

  17. Harder Practice

  18. Hardest Practice ( bonus?)

  19. Right Δ Trigonometry

  20. Right Δ Trigonometry MUST LABEL SIDES FROM ANGLE POINT OF VIEW Label Hypotenuse 1st. Then label side opposite of angle. The side left is your adjacent side.

  21. Right Δ Trigonometry No Tables Needed!

  22. Right Δ Trigonometry With both the TI 83 and 84 you need to make sure you are in degrees. With yellow TI 84, you need a ^^ after the angles to tell the calculator you are in degrees. But you do not need anything to solve for the inverse operations. Zoom equation takes care of it.

  23. Right Δ Trigonometry There are actually 6 functions with trignonmetry. However, the cosecant, secant, and cotangent are just the reciprocal of the sine, cosine, and tangent. When we do not know the degree of the angle, we can calculate the fraction ratio, then find the inverse of the ratio with the 2nd button on the calculator. This isn’t needed in zoom 400 and above. But in 300, divide the fraction, push 2nd then your 9 sine, cosine, or tangent button, then 2nd and (-) button for the answer of the fraction above.

  24. Angle of Elevation The angle of elevation is always measured from the ground up.  Think of it like an elevator that only goes up.  It is always INSIDE the triangle. In the diagram at the left, x marks the angle of elevation of the top of the tree as seen from a point on the ground. You can think of the angle of elevation in relation to the movement of your eyes.  You are looking straight ahead and you must raise (elevate) your eyes to see the top of the tree.

  25. Angle of Depression Theangle of depressionis alwaysOUTSIDEthe triangle. It is never inside the triangle. In thediagramat the left,xmarks the angle of depression of a boat at sea from the top of a lighthouse. You can think of the angle of depression in relation to the movement of your eyes. You are standing at the top of the lighthouse and you are looking straight ahead. You must lower (depress) your eyes to see the boat in the water. As seen in the diagram above of angle of depression, the dark black horizontal line is parallel to side CA of triangle ABC.  This forms what are called alternate interior angles which are equal in measure (so, x also equals the measure of  <BAC).Simply stated, this means that: the angle of elevation = the angle of depression. 

  26. Let’s Practice

  27. Let’s Practice

  28. Let’s Practice

  29. Let’s Practice

  30. Things to Remember These formulas ONLY work in a right triangle. LABEL everything you can LABEL!

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