Question

In a right triangle, if <0 = 53 and the side opposite to `/_θ` is equal to 2.3 meters, what is the approximate length of the hypotenuse?

Answer 1

The approximate length of the hypotenuse is 2.88 meters.

Explanation:

It is given that in a right angled triangle,
`{\theta}=53^(\circ)` and teh side opposite to
`{\theta}` is 2.3 meters, then using the trigonometry, we have

`(AB)/(AC)=sin53^(\circ)`

Substituting the given values, we have

`(2.3)/(x)=sin53^(\circ)`

⇒
`{(2.3)/(x)}=0.798`

⇒
`x=(2.3)/(0.798)`

⇒
`x=2.88 meters`

Thus, the approximate length of the hypotenuse is 2.88 meters.

Answer 2

2.8799

Explanation

θ = 53°

Opposite length to angle θ = 2.3 m

sinθ = opposite / hypotenuse

sin53 = 2.3/hypotenuse

hypotenuse = 2.3/sin53

= 2.3/0.7986

= 2.8799 m