Question

Find the missing side lengths. Leave your answers as radicals in simplest form.

10 POINTS!!! ANSWER PLZ

Answer 1

D.

`u =3`

`v =√(3)`

Explanation:

Given

The triangle in the diagram above

Required

Find the missing lengths, u and v

To find the missing lengths, we have to check the relationship between the missing lengths, the given length and the given angle;

From trigonometry;

`sin\ \theta = (Opp)/(Hyp)`; Where Opp = Opposite and Hyp = Hypotenuse

From the attached diagram;

`\theta = 30`

`Opp = v`

`Hyp = 2√(3)`

`sin\ \theta = (Opp)/(Hyp)` becomes

`sin\ 30 = (v)/(2√(3))`

Multiply both sides by
`2√(3)`

`2√(3) * sin\ 30 = (v)/(2√(3)) * 2√(3)`

`2√(3) * sin\ 30 = v`

In radians,
`sin30 = (1)/(2)`

`2√(3) * (1)/(2) = v`

`√(3) = v`

`v =√(3)`

Similarly, From trigonometry;

`cos\ \theta = (Adj)/(Hyp)`; Where Adj = Adjacent

From the attached diagram;

`\theta = 30`

`Adj = u`

`Hyp = 2√(3)`

`cos\ \theta = (Adj)/(Hyp)` becomes

`cos\ 30 = (u)/(2√(3))`

Multiply both sides by
`2√(3)`

`2√(3) * cos\ 30 = (u)/(2√(3)) * 2√(3)`

`2√(3) * cos\ 30 = u`

In radians,
`cos30 = (√(3))/(2)`

`2√(3) * (√(3))/(2) = u`

`√(3) * √(3) = u`

`3 = u`

`u =3`