Answer :

Answer:

cos V = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

cos V = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TV}{UV}[/tex]

We require to calculate UV

Using Pythagoras' identity in the right triangle

• c² = a² + b² ( c is the hypotenuse and a, b the legs )

let c = UV , a = TV , b = TU

UV² = TV² + TU² ( substitute values )

UV² = 10² + 24² = 100 + 576 = 676 ( take square root of both sides )

[tex]\sqrt{UV^2}[/tex] = [tex]\sqrt{676}[/tex]

UV = 26

Then

cos V = [tex]\frac{TV}{UV}[/tex] = [tex]\frac{10}{26}[/tex] = [tex]\frac{5}{13}[/tex]