SOLUTION: What is the sine, cosine and tangent of ∠E in the triangle shown in the image? Here is a link to the image: https://imgur.com/a/nNg4c1p

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Question 1183620: What is the sine, cosine and tangent of ∠E in the triangle shown in the image? Here is a link to the image: https://imgur.com/a/nNg4c1p
Answer by themasterofcircuits(27) About Me  (Show Source):
You can put this solution on YOUR website!
First, we need to be familiar with the following trigonometric ratios:
sin%28theta%29+=+opposite%2Fhypotenuse
cos%28theta%29+=+adjacent%2Fhypotenuse
tan%28theta%29+=+opposite%2Fadjacent
From Angle E, we have opposite = 8 and adjacent = 6.
We can find the hypotenuse using the Pythagorean Theorem:
a%5E2%2Bb%5E2=c%5E2, so c=sqrt%28a%5E2%2Bb%5E2%29=sqrt%288%5E2%2B6%5E2%29=sqrt%2864%2B36%29=sqrt%28100%29=10
So, we have that the hypotenuse = 10.
Plugging this information we have our ratios:
sin%28theta%29+=+opposite%2Fhypotenuse=8%2F10
cos%28theta%29+=+adjacent%2Fhypotenuse=6%2F10
tan%28theta%29+=+opposite%2Fadjacent=8%2F6
Reducing, we have:
sin%28theta%29+=+4%2F5
cos%28theta%29+=+3%2F5
tan%28theta%29+=+4%2F3