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

Answer:

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.

Step-by-step 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

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

$sin\theta =Sin 30^o=\frac{AB}{AC},(Sin 30^o=\frac{1}{2})$

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

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.