Question

In triangle TUV, the measure of angle V is 90 degrees, TV = 33, UT = 65, and VU = 56. What ratio represents the cosine of angle U

Answer 1

In triangle TUV, with angle V being the right angle, we have:

- \( TV = 33 \) (the side opposite angle U)
- \( UT = 65 \) (the side opposite angle V)
- \( VU = 56 \) (the side opposite angle T)

To find the cosine of angle U, we use the definition of cosine in a right triangle, which is given by:

\[
\cos(U) = \frac{\text{adjacent side to angle U}}{\text{hypotenuse}}
\]

In triangle TUV:
- The side adjacent to angle U is \( VU \) (which has length 56).
- The hypotenuse is \( UT \) (which has length 65).

Thus, the cosine of angle U is:

\[
\cos(U) = \frac{VU}{UT} = \frac{56}{65}
\]

So the ratio that represents the cosine of angle U is:

\[
\frac{56}{65}
\]