Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of si
n 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.
1 answer:
Using trigonometric relations, we will see that for the given right triangle:
sin(x°) = 3/5
cos(y°) = 3/5
<h3>How to find the wanted values?</h3>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:
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:
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