Question

In the 30-60-90 triangle below, side s has a length of Blank and the hypotenuse has a length of blank?

Answer 1

the answer is D

`√(3) \: and \: 2`

Answer 2

The length of bank side ,s =
`√(3)` unit.

The length of hypotenuse, h= 2 unit.

Explanation:

Given in 30-69-90 triangle

We know that

`tan\theta= \frac {perpendicular}{base}`

`sin\theta=\frac { perpendicular}{ hypotenuse}`

When
`\theta=30^(\circ)`

`sin\theta= (1)/(h)`

`sin30^(\circ)=\frac {1}{h}`

`sin30^(\circ)=(1)/(2)`

Therefore,
`(1)/(h) =(1)/(2)`

By cross multiply we get

h=2

`tan30^(\circ)=(1)/(s)`

`tan30^(\circ)=\frac {1}{√(3)}`

`(1)/(s) =(1)/(√(3))`

By cross multiply we get

s=
`√(3)`

Hence, the length of side of bank, s=
`√(3)` unit

Length of hypotenuse ,h=2 unit.