Question

Express tan KK as a fraction in simplest terms.
I
J
K
8
10

Answer 1

I don't have the diagram, so I need to know which side each number labels. Here are the likely cases — pick the one that matches your figure:

- If 10 is the hypotenuse and 8 is the leg opposite angle K:
opposite = 8, adjacent = sqrt(10^2 − 8^2) = sqrt(100 − 64) = 6, so tan K = 8/6 = 4/3.

- If 10 is the hypotenuse and 8 is the leg adjacent to angle K:
adjacent = 8, opposite = sqrt(100 − 64) = 6, so tan K = 6/8 = 3/4.

- If 8 and 10 are the two legs and 8 is the opposite while 10 is the adjacent:
tan K = 8/10 = 4/5.

Tell me which side is which (or paste the picture) and I'll give the single correct value.