Question

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share? A right triangle is shown with one leg measuring 4 and another leg measuring 3. The angle across from the leg measuring 3 is marked x degrees, and the angle across from the leg measuring 4 is marked y degrees.

Answer 1

Using trigonometric relations, we will see that for the given right triangle:

sin(x°) = 3/5

cos(y°) = 3/5

How to find the wanted values?

Remember that for a right triangle for any of the internal angles that are not 90°.

sin(a) = (opposite cathetus)/(hypotenuse)

cos(a) = (adjacent cathetus)/(hypotenuse).

In this case, the two cathetus measure 4 units and 3 units, so the hypotenuse measures:

$H = \sqrt{4^2 + 3^2} = 5$

Then for x°, the opposite cathetus measures 3 units, then we have:

sin(x°) = 3/5

And for y°, the adjacent cathetus also measures 3 units, so:

cos(y°) = 3/5

These are equal because both depend on the same cathetus of the right triangle.

If you want to learn more about right triangles:

brainly.com/question/2217700

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