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 $\sqrt{3}$

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:

$\sin \theta=\frac{Perpendicular}{Hypotenuse}$

Given:

$\theta =30^o$

Hypotenuse = 2

$\sin 30^o=\frac{AB}{2}$

As, we know that $\sin 30^o=\frac{1}{2}$

$\frac{1}{2}=\frac{AB}{2}$

$AB=1$

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

According to trigonometric function:

$\sin \theta=\frac{Perpendicular}{Hypotenuse}$

Given:

$\theta =60^o$

Hypotenuse = 2

$\sin 60^o=\frac{BC}{2}$

As, we know that $\sin 60^o=\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}=\frac{BC}{2}$

$BC=\sqrt{3}$

Thus, the length of the other two sides AB and BC is, 1 and $\sqrt{3}$