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In this activity you will use your knowledge of the three main trig ratios to solve for missing sides of right triangles. Recall the three main trig ratios. tangent = cosine = Sine = hypotenuse hypotenuse opposite adjacent adjacent opposite Drag and drop the correct values to show each trig ratio. tangent = cosine = Sine = hypotenuse ? hypotenuse opposite adjacent ? opposite ? adjacent Drag and drop each trig function with the correct ratio. Answer carefully! tangent ? cosine ? sine ? = = = hypotenuse adjacent hypotenuse opposite adjacent opposite Recall, these formulas can be remember by using C stands for cosine S stands for sine T stands for tangent SOH CAH TOA A stands for adjacent O stands for opposite H stands for hypotenuse Each of these triangles has a right angle Next, you have to be able to label the right triangle. and an acute angle that is marked. Here are two example triangles The last side is the adjacent, next to the marked angle The opposite is the side across from the marked angle The hypotenuse is the side across from the right angle Next, you have to be able to label the right triangle. Here are two example triangles Hyp Opp Adj Adj Hyp Opp Drag and drop the values onto the right triangle diagram. Hyp ? Opp ? Adj ? Solve for "x" in the right triangle using a trig ratio. Consider how you would solve this problem. 35∘ 9 x Drag and drop the correct values in reference to the 35º angle. First, look at the sides involved in the problem hypotenuse ? adjacent ? 35∘ 9 x opposite ? Which trig ratio should we use to solve for "x"? sine cosine tangent Hyp 35∘ 9 Adj x Opp Write an equation involving sine of 35º to solve for x. sin 35∘ = Hyp 35∘ 9 Adj x Opp Use algebra skills to solve for x. sin 35∘ = x 9 35∘ 9 x x = 9 ÷ (sin 35) x = 9 + sin(35) x = 9*sin(35) Use a calculator to solve for x. Round to the nearest hundredth. sin 35∘ = x 9 35∘ 9 x x = x = 9*sin(35) units sine cosine tangent Which Trig Ratio should you use to solve for x? 15∘ 3 x Which Trig Ratio should you use to solve for x? 20 75∘ x sine cosine tangent sine cosine tangent Which Trig Ratio should you use to solve for x? 77∘ x 3 Solve for x in this right triangle. First label the sides in relation to the 70º angle. Hyp ? Opp ? x 6 70∘ Adj ? Choose the trig ratio sine cosine tangent Hyp Opp x 6 70∘ Adj Write an equation to solve for x. sin = Hyp Opp 6 ? x ? x 6 70∘ Adj Rewrite the equation to solve for x. sin 70 = 6 x Hyp Opp x x = 6*sin(70) x = 6/(sin70) x = 6 + sin(70) 6 70∘ Adj Solve for x. (Round to the nearest tenth.) x = 6 / (sin70) sin 70 = 6 / x Hyp Opp x 6 70∘ x = Adj units Solve for x in this right triangle. First label the sides in relation to the 75º angle. Opp ? Hyp ? 9 75∘ x Adj ? Choose the correct trig ratio. Opp Hyp 9 75∘ x Adj sine cosine tangent Write an equation. Then solve for x. cos Opp Hyp = 9 x ? 9 ? 75∘ x Adj Solve for x. Round to the tenths place. x = units |