Question

For context, there is a right triangle, leg a, leg b, and the hypotenuse, labeled c, the angle where leg a and the hypotenuse is an angle labeled with the symbol that is a o with a / in the middle of it, and a 0 with a horizontal line within it

if a = 6 in, and 0 = 45, find the value of c. Round your answer to the nearest hundredth.

Answer 1

In a right triangle, you can use the relationship between the sides and angles to find the hypotenuse. You mentioned that angle O (which I assume is the angle opposite leg a) is 45 degrees, and leg a (the side opposite this angle) is 6 inches.

Since the angle is 45 degrees and leg a is opposite this angle, it also means that leg b is equal to leg a due to the properties of a 45-45-90 triangle.

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse can be calculated using the formula:
\[
c = a \sqrt{2}
\]

Given that \( a = 6 \) inches:

\[
c = 6 \sqrt{2}
\]

Now, calculate \( \sqrt{2} \):
\[
\sqrt{2} \approx 1.414
\]

Now substitute this into the equation for c:

\[
c = 6 \times 1.414 \approx 8.484
\]

Now, rounding to the nearest hundredth:

\[
c \approx 8.48 \text{ inches}
\]

So, the value of the hypotenuse \( c \) rounded to the nearest hundredth is **8.48 inches**.