Question

In a right triangle where one of the angles measure 30° what is the ratio of the length of the side opposite the 30°angle to the length of the side opposite the 90°angle?

Answer 1

The ratio of the length of the side opposite the 30°angle to the length of the side opposite the 90°angle is 1:2.

Explanation:

Consider ABC, With 90° angle at B and 30° angle at C.

To find: AB:AC=?

Solution:

AB = perpendicular of the right angled triangle

AC = Hypotenuse of the triangle

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

`sin\theta =Sin 30^o=(AB)/(AC),(Sin 30^o=(1)/(2))`

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

The ratio of the sides ,AB:AC = 1:2.

Hence,the ratio of the length of the side opposite the 30°angle to the length of the side opposite the 90°angle is 1:2.