In a right triangle, if one angle is 30°, what is the ratio of the lengths of th

₹0.0

Question: In a right triangle, if one angle is 30°, what is the ratio of the lengths of the sides opposite to the 30° and 90° angles?

Options:

Correct Answer: 1:2

Solution:

In a 30-60-90 triangle, the side opposite the 30° angle is half the hypotenuse, giving a ratio of 1:2.

In a right triangle, if one angle is 30°, what is the ratio of the lengths of the sides opposite to the 30° and 90° angles?

In a right triangle, if one angle is 30°, what is the ratio of the lengths of the sides opposite to the 30° and 90° angles?

Step 1: Understand that in a right triangle, one angle is 90° and the other two angles add up to 90°.
Step 2: Recognize that if one angle is 30°, the other angle must be 60° (because 90° - 30° = 60°).
Step 3: Know that this type of triangle is called a 30-60-90 triangle.
Step 4: In a 30-60-90 triangle, the side opposite the 30° angle is always half the length of the hypotenuse (the side opposite the 90° angle).
Step 5: Therefore, if we let the length of the hypotenuse be 2 units, the side opposite the 30° angle will be 1 unit.
Step 6: This gives us a ratio of the side opposite the 30° angle (1) to the hypotenuse (2), which is 1:2.

30-60-90 Triangle Ratios – In a 30-60-90 triangle, the sides are in a specific ratio: the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is the hypotenuse multiplied by √3/2.