If the angles of a triangle are 30°, 60°, and 90°, and the shortest side is 5 cm

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Question: If the angles of a triangle are 30°, 60°, and 90°, and the shortest side is 5 cm, what is the length of the longest side?

Options:

Correct Answer: 10 cm

Solution:

In a 30-60-90 triangle, the longest side (hypotenuse) is twice the shortest side: 2 * 5 = 10 cm.

If the angles of a triangle are 30°, 60°, and 90°, and the shortest side is 5 cm, what is the length of the longest side?

If the angles of a triangle are 30°, 60°, and 90°, and the shortest side is 5 cm, what is the length of the longest side?

Step 1: Identify the type of triangle. This triangle has angles of 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 side opposite the 60° angle is 'x√3', and the longest side (hypotenuse) is '2x'.
Step 3: Identify the shortest side. The shortest side is given as 5 cm, which corresponds to 'x'.
Step 4: Calculate the longest side (hypotenuse). According to the properties, the longest side is '2x'. So, we calculate it as 2 * 5 cm.
Step 5: Perform the calculation. 2 * 5 = 10 cm.
Step 6: State the length of the longest side. The longest side of the triangle is 10 cm.

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 side opposite the 60° angle is x√3, and the hypotenuse (opposite the 90° angle) is 2x.