Question

Need Help ASAP !
Topic is trigonometric ratios.

Answer 1

`\cos(T)` =
`(√(15))/(5)`

Explanation:

Given parameters.

`TU = 4\sqrt 5`

`SU = 4\sqrt 2`

`ST = 4\sqrt 3`

Required

Determine
`\cos(T)`

Reference to
`\angle T`, we have:

`Opposite = 4\sqrt 2`

`Adjacent = 4\sqrt 3`

`Hypotenuse = 4\sqrt 5`

Apply trigonometry ratio of cosine

`\cos(T)`
`= (Adjacent)/(Hypotenuse)`

Substitute values for Adjacent and Hypotenuse

`\cos(T)`
`= (4\sqrt 3)/(4\sqrt 5)`

`\cos(T)`
`= (\sqrt 3)/(\sqrt 5)`

Rationalize:

`\cos(T)`
`= (\sqrt 3)/(\sqrt 5)*(\sqrt 5)/(\sqrt 5)`

`\cos(T)` =
`(√(15))/(5)`