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

Question

asked Feb 26, 2020 67.3k views

2 Answers

Mahmud Adam · Answer 1 · 2020-03-01T12:05:10+0000

Answer:

The length of bank side ,s =
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=

Hence, the length of side of bank, s=
unit

Length of hypotenuse ,h=2 unit.