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9.5 Trig Ratios HMWK: p. 562, #s 13-37 odd, 38, 39 Game Plan: Today I will be able to use Trig Ratios to determine side lengths of triangles. Warm-up: Solve for the missing length. 9.5 Trig Ratios Applications ~ Special Rt. The roof of a doghouse is shaped like an equilateral triangle with height 3 feet. Estimate the area of the cross-section of the roof. Steps 3 ft 1. Use spec. tri. relationships to find base of triangle 2. Use area formula 5.2 ft. Trig Ratios Origin of SOH CAH TOA 9.5 Trig Ratios Trig Ratios Trigonometry – Greek for “measure of triangles” Trig Ratios – ratio of lengths of sides of rt. triangle Uses acute angles Basic trig ratios Sine (sin) Cosine (cos) Tangent (tan) 9.5 Trig Ratios SOH CAH TOA SOH OPP sin HYP B CAH cos ADJ HYP TOA OPP tan ADJ 42° C A 9.5 Trig Ratios Using Trig Ratios ~ Sides SOH CAH TOA B OPP 3 sin A .6000 HYP 5 a=3 ADJ 4 cos A .8000 HYP 5 c=5 46° C b=4 A tan A OPP 3 .7500 ADJ 4 Round to 4 decimals places! Find trig ratios for angle B. 9.5 Trig Ratios Using Trig Ratios ~ Angles Make sure calculator is in DEGREE mode “MODE” and check 3rd line down Use calculators to find following measures. 1. sin37° 2. cos37° 3. tan37° 9.5 Trig Ratios Trig Ratios ~ Angles B Sketch the given right triangle ABC, if mA=46°, mC=90° and a=7. Find the length of sides b and c. 7 SOH CAH TOA c 1. Set up all trig ratios 2. Determine which ratio to use 46° C b A 3. Solve for variable 9.5 Trig Ratios Applications You are measuring the height of a building. You stand 100 feet from the base of the building. You measure the angle of elevation from a point on the ground to the top of the building to be 48°. Estimate the height of the building. Be sure to … • sketch the problem • label the problem • SOH CAH TOA 9.5 Trig Ratios Inverse Trig Ratios Used to find angle measures of right triangles. Sin-1, cos –1 , tan –1 9.5 Trig Ratios Wrap-Up Right Triangles … Altitude Geometric Mean Pythagorean Thm Converse of Pyth Thm Special Right Triangles Trig Ratios