A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5, wh

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Question: A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5, what is the length of the hypotenuse?

Options:

Correct Answer: 10

Solution:

In a 30-60-90 triangle, the hypotenuse is twice the shortest side. Therefore, hypotenuse = 2 * 5 = 10.

A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5, what is the length of the hypotenuse?

A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5, what is the length of the hypotenuse?

Step 1: Identify the type of triangle. This triangle has angles measuring 30°, 60°, and 90°, which makes it a 30-60-90 triangle.
Step 2: Understand the properties of a 30-60-90 triangle. In this type of triangle, the sides have a specific ratio: the shortest side (opposite the 30° angle) is 'x', the longer side (opposite the 60° angle) is 'x√3', and the hypotenuse (opposite the 90° angle) is '2x'.
Step 3: Identify the shortest side. The problem states that the shortest side is 5.
Step 4: Use the property of the hypotenuse. Since the hypotenuse is twice the shortest side, calculate it as follows: hypotenuse = 2 * shortest side.
Step 5: Substitute the value of the shortest side into the equation: hypotenuse = 2 * 5.
Step 6: Perform the multiplication: hypotenuse = 10.

30-60-90 Triangle Properties – In a 30-60-90 triangle, the sides are in a specific ratio: the shortest side (opposite the 30° angle) is x, the longer leg (opposite the 60° angle) is x√3, and the hypotenuse (opposite the 90° angle) is 2x.