Given the right triangle below, evaluate cosθ\cos\thetacosθ.

cos ⁡ θ = 15 17 \cos\theta=\frac{15}{17} cos θ = 17 15

Given the right triangle below, evaluate cos θ \cos\theta cos θ .

Hey, everyone. So let's try solving this problem. Here it says, given the right triangle below, evaluate the cosine of theta, which is this angle. So let's see what we can do. Now in order to solve this problem, you need to remember SohCahToa. SOHCAHTOA is a memory tool that we use to recall the trigonometric functions and how they relate to a right triangle. Now in this case, we have the sine, cosine, and tangent. And since I can see that we are asked to find the cosine of theta, what I'm going to do is use this relationship right here. This tells us that the cosine of our angle theta is equal to adjacent over hypotenuse. So this tells us how the sides of the triangle relate to our cosine function. And what we can do to find these sides is we can look at our angle theta because that's what this cosine is, and we can see that the adjacent side to this angle is 15. So that means that we're going to have 15, and then this is going to be divided by the hypotenuse, which is the long side or 17. So the cosine of our angle theta is 15 over 17, and that is the answer to this problem. So hope you found this video helpful. Thanks for watching.

Given the right triangle below, evaluate cos ⁡ θ \cos\theta cos θ .

cos ⁡ θ = 15 17 \cos\theta=\frac{15}{17} cos θ = 17 15

cos ⁡ θ = 8 17 \cos\theta=\frac{8}{17} cos θ = 17 8

cos ⁡ θ = 8 15 \cos\theta=\frac{8}{15} cos θ = 15 8

cos ⁡ θ = 15 8 \cos\theta=\frac{15}{8} cos θ = 8 15

12. Trigonometric Functions

Trigonometric Functions on Right Triangles

Business Calculus

12. Trigonometric Functions

Trigonometric Functions on Right Triangles

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Multiple Choice

Given the right triangle below, evaluate $\cos\]\theta$ .

$\cos\]\theta\)=\(\frac{8}{17}$

$\cos\]\theta\)=\(\frac{8}{15}$

$\cos\]\theta\)=\(\frac{15}{17}$

$\cos\]\theta\)=\(\frac{15}{8}$

Verified step by step guidance

Step 1: Recall the definition of cosine in a right triangle. Cosine of an angle θ is defined as the ratio of the length of the adjacent side to the hypotenuse: cos(θ) = adjacent/hypotenuse.

Step 2: Identify the sides of the triangle relative to angle θ. From the image, the adjacent side to θ is 15, the opposite side is 8, and the hypotenuse is 17.

Step 3: Substitute the values into the formula for cosine. Using cos(θ) = adjacent/hypotenuse, we have cos(θ) = 15/17.

Step 4: Verify the calculation. Ensure that the adjacent side and hypotenuse are correctly identified and the ratio is simplified if necessary.

Step 5: Compare the calculated value of cos(θ) = 15/17 with the given options to confirm the correct answer.

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Struggling with Business Calculus?

Given the right triangle below, evaluate cosθ\(\cos\]\theta\)cosθ.

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Trigonometric Functions on Right Triangles practice set

Given the right triangle below, evaluate $\cos\]\theta$ .