Apply the 30º-60º-90º Triangle Theorem. If the length of the shorter leg a of the triangle is 4 inches, what is the measure of the length of the longer leg b for the triangle to the nearest inch.

Answer 1

In a 30º-60º-90º triangle, the sides are in a specific ratio relative to each other:

• The length of the shorter leg (opposite the 30º angle) is \( a \).
• The length of the longer leg (opposite the 60º angle) is \( a \sqrt{3} \).
• The length of the hypotenuse is \( 2a \).

Given that the shorter leg \( a \) is 4 inches, we can find the length of the longer leg \( b \) using the ratio:

\[ b = a \sqrt{3} = 4 \sqrt{3} \]

Now, we will calculate \( 4 \sqrt{3} \):

\[ \sqrt{3} \approx 1.732 \] \[ b \approx 4 \times 1.732 \approx 6.928 \]

Rounding \( 6.928 \) to the nearest inch gives us:

\[ b \approx 7 \text{ inches} \]

Thus, the length of the longer leg \( b \) is approximately 7 inches.