Question

Find the unknown length in the right triangle. If​ necessary, round to the nearest tenth.
nbsp 17 ft
30 ft nbsp
Question content area bottom
Part 1
A.
24.7 ft
B.
305.5 ft
C.
611 ft
D.
23.5 ft

Answer 1

To find the unknown length in a right triangle, we can apply the Pythagorean theorem, which states:

\[ a^2 + b^2 = c^2 \]

where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.

From your question, it seems we have the lengths of two sides of a right triangle:

- One side is 17 ft
- The other side is 30 ft

Since both values are provided, we can assume these are the lengths of the legs of the triangle, and we need to calculate the hypotenuse.

Now we can use the Pythagorean theorem:

1. Let \( a = 17 \) ft and \( b = 30 \) ft.
2. Plugging in the values:
\[
c^2 = a^2 + b^2
\]
\[
c^2 = 17^2 + 30^2
\]
\[
c^2 = 289 + 900
\]
\[
c^2 = 1189
\]
3. Now, take the square root to find \( c \):
\[
c = \sqrt{1189} \approx 34.5 \text{ ft}
\]

It seems there is some misunderstanding because the options provided do not include the calculated hypotenuse. Let's check whether you're looking for the length of one of the legs instead.

If 30 ft is the hypotenuse and we're solving for one leg, we can rearrange the equation:

1. Let \( c = 30 \) ft (hypotenuse) and \( a = 17 \) ft.
\[
30^2 = 17^2 + b^2
\]
\[
900 = 289 + b^2
\]
\[
b^2 = 900 - 289
\]
\[
b^2 = 611
\]
2. Taking the square root to get \( b \):
\[
b = \sqrt{611} \approx 24.7 \text{ ft}
\]

Thus, the unknown length is approximately **24.7 ft** (Option A).