△ABC is a 30-60-90 triangle where m∠B=90° . The length of the shorter leg is 11 units. What is the length of the hypotenuse? Enter your answer in the box

In a 30-60-90 right triangle, the ratio of the lengths of the sides is 1 : √3 : 2. This means that the shorter leg (opposite the 30° angle) is 1 part, the longer leg (opposite the 60° angle) is √3 parts, and the hypotenuse (opposite the 90° angle) is 2 parts.

You mentioned that the shorter leg is 11 units. Since the shorter leg corresponds to 1 part in the ratio, to find the length of the hypotenuse (which is 2 parts in the ratio), we just need to double the length of the shorter leg.

Therefore, the hypotenuse is 11 units * 2 = 22 units.

Extra: A 30-60-90 triangle is one of the special right triangles defined by the specific ratios of its sides. Remembering these ratios can make solving problems with 30-60-90 triangles much easier. The ratios stem from the geometric relationships within the triangle:

- The shortest side, opposite the 30° angle, is considered to be x. - The side opposite the 60° angle, which is the longer leg, is x√3. - And the side opposite the 90° angle, which is the hypotenuse, is 2x.

These relationships can help you find the lengths of unknown sides given any one side. In practical problems, such as in construction or physics, recognizing these types of triangles can be very useful for calculating distances or for understanding the forces at work within a particular structure.