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Learn about right triangles, identifying sides, and calculating trigonometric ratios like sine, cosine, and tangent. Understand SOH-CAH-TOA rule for easy solutions.
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1. Review Triangle Key Terms • A right triangle is any triangle with a right angle • The longest and diagonal side is the hypotenuse • The other two sides are the opposite side and adjacent side (means next to) • The labels depend on the reference angle
1. Identifying Sides of Right Triangle for a Reference Angle Ex 1: Reference Angle A; Identify the Sides (I DO) Reference Angle: A Hypotenuse: Adjacent Side: Opposite Side: AB Hypotenuse AC Opposite BC Adjacent B B Ex 2: Reference Angle B; Identify the Sides (WE DO) Reference Angle: B Hypotenuse: Adjacent Side: Opposite Side: AB Hypotenuse AC Adjacent BC C C A A Opposite
2. Finding the Value of Trigonometric Ratios • There are three main Trigonometric Ratios • SINE of an ANGLE = __OPPOSITE__ • HYPOTENUSE • COSINE of an ANGLE = ADJACENT__ • HYPOTENUSE • TANGENT of an ANGLE = __OPPOSITE__ • ADJACENT • Remember, SOH – CAH – TOA
2. Finding the Value of Trigonometric Ratios Ex 3: Find the Value of Sin A (I DO) Reference Angle: A Opposite=4; Hypotenuse=5 Sin A = Opp = 4 = 0.80 Hyp 5 Sin A = 0.80 Hyp. 5 Opp 4 3 FIRST, LABEL ALL SIDES! SOH CAH TOA Adj B B Ex 4: Find the Value of Cos A (WE DO) Reference Angle: A Adjacent; 3 Hypotenuse=5 Cos A = Adj = 3 = 0.60 Hyp 5 Cos A = 0.60 Hyp. 5 Opp 4 C C A A 3 Adj
2. Finding the Value of Trigonometric Ratios Ex 3: Find the Value of Cos B (WE DO) Reference Angle: B Opposite=4; Hypotenuse=5 Cos B = Adj = 4 = 0.80 Hyp 5 Cos B = 0.80 Hyp. 5 Adj 4 3 FIRST, LABEL ALL SIDES! SOH CAH TOA Opp B B Ex 4: Find the Value of Tan B (WE DO) Reference Angle: B Opposite=3; Adjacent=4 Tan B = Opp = 3 = 0.75 Adj 4 Tan B = 0.75 Hyp. 5 Adj 4 C C A A 3 Opp