Question

Triangle A B C is shown. Angle A C B is a right angle, angle C A B is 60 degrees, and angle A B C is 30 degrees. The length of the hypotenuse is 10.
What are the lengths of the other two sides of the triangle?

Answer 1

Answer:

5/3

Step-by-step explanation:

Answer 2

Answer : The lengths of the other two sides of the triangle is, 5 and $5\sqrt{3}$

Step-by-step explanation :

Given:

∠ACB = 90°

∠CAB = 60°

∠ABC = 30°

Length of hypotenuse = 10

According to trigonometric function,

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

First we have to calculate the length AC.

$\sin 30^o=\frac{Perpendicular}{Hypotenuse}$

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

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

$\frac{1}{2}=\frac{AC}{10}$

$AC=5$

Now we have to calculate the length CB.

$\sin 60^o=\frac{Perpendicular}{Hypotenuse}$

$\sin 60^o=\frac{CB}{AB}$

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

$\frac{\sqrt{3}}{2}=\frac{CB}{10}$

$CB=5\sqrt{3}$

Therefore, the lengths of the other two sides of the triangle is, 5 and $5\sqrt{3}$