Question

A rope is stretched from the top of a 7-foot tent to a point on the ground that is 10 feet from the base of the tent.
tent with triangle
How long is the rope? Approximate to the nearest tenth if necessary.

A.
3 ft
B.
17 ft
C.
7.1 ft
D.
12.2 ft

Answer 1

To find the length of the rope, we can model the situation as a right triangle, where:

- One vertical leg of the triangle is the height of the tent (7 feet).
- The other leg is the horizontal distance from the base of the tent to the point on the ground (10 feet).
- The rope acts as the hypotenuse of the triangle.

We can use the Pythagorean theorem for this calculation:

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

where:
- \(c\) is the length of the hypotenuse (the rope),
- \(a\) is one leg of the triangle (height of the tent = 7 feet),
- \(b\) is the other leg of the triangle (horizontal distance = 10 feet).

Now plugging in the numbers:

\[
c^2 = 7^2 + 10^2
\]
\[
c^2 = 49 + 100
\]
\[
c^2 = 149
\]
\[
c = \sqrt{149}
\]

Calculating \(\sqrt{149}\):

\[
c \approx 12.2 \text{ feet}
\]

Thus, the length of the rope is approximately \(12.2\) feet.

The correct answer is **D. 12.2 ft**.