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Warm up: Solve for θ

Warm up: Solve for θ. θ. 11. 7. Welcome to the wonderful world of TRIANGLES!. WARNING:. Today’s material ONLY applies to Right Triangles. Soon we will be working with non-right triangles, and will not be able to use these rules. LABELS

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Warm up: Solve for θ

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  1. Warm up: Solve for θ θ 11 7

  2. Welcome to the wonderful world of TRIANGLES!

  3. WARNING: • Today’s material ONLY applies to Right Triangles. • Soon we will be working with non-right triangles, and will not be able to use these rules.

  4. LABELS • When we label triangles, we typically use CAPITAL letters for the Angles, and lower case letters for the sides. • The letter on the side should correspond to the opposite angle.

  5. The side opposite the right angle is always the hypotenuse. • Given an angle θ, the side touching it is called the “adjacent” side, and the side opposite it is the “opposite” side.

  6. Sin, Cos, Tan • Sine, Cosine and Tangent are all trigonometric functions. They come from the “Unit Circle”. You will learn more about them as functions in Pre-Calc. • We will not go into depth about the functions themselves, instead we will use our handy dandy calculators! 

  7. Now we are ready for SohCah Toa • We use SoaCah Toa to find missing angles AND missing side lengths of right triangles. • To find a missing angle, you need at least 2 side lengths. • To find a missing side length, you need either the other two side lengths, or one side length and one angle (2 things total).

  8. SohCah Toa Cos Tan

  9. Example 1: Solve for θ. Well, first we need to figure out what position each number is in relation to the angle we want to find: 30 = opposite side 35= hypotenuse. Then we ask, of SohCah Toa, which uses opp and hyp? Sin! Then we simply plug the numbers in and solve. .85714….. 35 30 θ

  10. Example 1 Cont…Uh Oh! One more step. .85714….. But we don’t want the Sin of θ, we want θ. Now we need our calculators. To get θ by itself, we will use “Sin Inverse”, which looks like . (.85714…) = 58.98°, and so θ = 58.98°.

  11. Check your calculator! • Didn’t get that answer? • Make sure your calculator is in the “degree” mode. • Go to mode, and if it is in “radians” switch it to degrees.

  12. Now you Try! Find θ: θ 12 37

  13. Solution: • Tan • Tan • Tan • θ • θ=72.03° θ 72.03° 12 12 37 37

  14. You Try Again! • Find the Sin, Cos and Tan Ratios for θ. • Note: Do not actually solve for θ. 70 32 θ 55

  15. Solution Cos Tan 70 32 θ 55

  16. Homework • Page 489 • Problems: 1, 4, 5,

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