Question

In ΔTUV, the measure of ∠V=90°, UT = 65, VU = 56, and TV = 33. What ratio represents the cosine of ∠T?

Answer 1

Answer: The ratio that represents the cosine of ∠T is
`(56)/(65)`

Explanation:

We are given:

UV = 56 units

VT = 33 units

UT = 65 units

∠V = 90°

Cosine of an angle is equal to the ratio of base and the hypotenuse of the triangle. ΔTUV is drawn in the image below.

`\cos \theta=\frac{\text{base}}{\text{hypotenuse}}`

Base of the triangle is UV and the hypotenuse of the triangle is TU

Putting values in above equation, we get:

`\cos \theta=(UV)/(TU)=(56)/(65)`

Hence, the ratio that represents the cosine of ∠T is
`(56)/(65)`