1020 Apply trig ratios to find missing side

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10/20: Apply trig ratios to find missing side lengths of right triangles Do Now

10/20: Apply trig ratios to find missing side lengths of right triangles Do Now Agenda On your desk: - Pencil & Calculator DO NOW! & Check -Today’s Handouts Guided Practice Independent Practice DO NOW! Homework! (maybe…) Homework Handout (8 problems) Parent-Teacher Conferences TONIGHT! 3 PM – 9 PM!

We will learn to… • Apply trig ratios to find missing side lengths of

We will learn to… • Apply trig ratios to find missing side lengths of right triangles.

Trigonometric Ratios Review: Sine Ratio: sin = Cosine Ratio: cos = Tangent Ratio: tan

Trigonometric Ratios Review: Sine Ratio: sin = Cosine Ratio: cos = Tangent Ratio: tan = opposite hypotenuse adjacent hypotenuse opposite adjacent A pneumonic to help remember trig ratios is… SOH CAH TOA

Example 1: Find the value of x. Round to tenth. Given: Right Triangle Opposite

Example 1: Find the value of x. Round to tenth. Given: Right Triangle Opposite Side = 11 Angle = 32⁰ Finding: Adjacent Side = x Trig Ratio: Tangent Write Equation, Substitute, & Solve: tan = opposite adjacent 11 x tan 32° = x x x tan 32° = 11 tan 32° 11 x = tan 32° x ≈ 17. 6 units

Example 2: Use your value of x to find the area of the triangle

Example 2: Use your value of x to find the area of the triangle above. Round to the nearest whole unit. Area of Triangle = bh or 2 17. 6 A = 17. 6(11) 2 A ≈ 97 units b = base h = height

Example 3: Find the value of x and then y. Round to hundredth. 12.

Example 3: Find the value of x and then y. Round to hundredth. 12. 08 a 2 + b 2 = c 2 12. 082 + y 2 = 162 y 2 = 110. 07 y ≈ 10. 49 Given: Solve: opposite How else could we have - Right Triangle sin = solved for y after finding hypotenuse - Hypotenuse = 16 of x? the value x sin 49° = 16 - Angle = 49⁰ 16 16 sin 49° = x Finding: - Opposite Side = x - Adjacent Side = y Trig Ratio: - Sine (for x) - Cosine (for y) x ≈ 12. 08 units cos = adjacent hypotenuse y cos 49° = 16 16 16 cos 49° = y y ≈ 10. 50 units