Question

Suppose a right triangle has a hypotenuse of length 2 and one angle is 30 degrees. find the length of the other two sides

Answer 1

ABC
AB=2
∠B=30°
AC=AB*sin30°=2*(1/2)=1
AB²=AC²+BC²⇒
BC=√(AB²-AC²)=√(2²-1²)=√3≈1,7

Answer 2

Answer : The length of the other two sides AB and BC is, 1 and
`√(3)`

Step-by-step explanation :

First we have to calculate the angle A.

In right angle ΔABC,

Let ∠B = 30°

∠C = 90°

As we know that, the sum of interior angle of a triangle is 180°

∠A + ∠B + ∠C = 180°

∠A + 30° + 90° = 180°

∠A = 60°

Now we have to calculate the length AB in right angle ΔABC.

According to trigonometric function:

`\sin \theta=(Perpendicular)/(Hypotenuse)`

Given:

`\theta =30^o`

Hypotenuse = 2

`\sin 30^o=(AB)/(2)`

As, we know that
`\sin 30^o=(1)/(2)`

`(1)/(2)=(AB)/(2)`

`AB=1`

Now we have to calculate the length BC in right angle ΔABC.

According to trigonometric function:

`\sin \theta=(Perpendicular)/(Hypotenuse)`

Given:

`\theta =60^o`

Hypotenuse = 2

`\sin 60^o=(BC)/(2)`

As, we know that
`\sin 60^o=(√(3))/(2)`

`(√(3))/(2)=(BC)/(2)`

`BC=√(3)`

Thus, the length of the other two sides AB and BC is, 1 and
`√(3)`