Question

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**.