Question

The hypotenuse of a 30°-60°-90° triangle measures 10 inches. Which could be the length of a leg of the triangle?​

Answer 1

Answer:

6 and 8

Step-by-step explanation:

The hypotenuse of a 30°-60°-90° triangle measures 10 inches.

To find the length of one of the legs, we use the idea of Pythagorean Triples.

Pythagorean Triples are any set of three numbers that satisfies the Pythagorean Theorem. Some common examples are:

• 3, 4 and 5
• 5, 12 and 13
• 9, 40 and 41

Note that in a Pythagorean Triple,

• The longest length is always the Hypotenuse.
• New Triples can be formed from product of existing triples.

In our given triangle, the Hypotenuse=10 Inches

Consider the Pythagorean Triple 3,4, and 5

• 5 is the Hypotenuse
• Multiply the Triples by 2, we obtain:
• 6, 8 and 10 (in which 10 is the hypotenuse)

Therefore, 6 and 8 could be the length of a leg of the 30°-60°-90° triangle.