Question

Simon set up his tent in his backyard last night. His tent is 6 feet tall. To secure it to the ground, he attached a rope from the top of the tent to the ground 8 feet away from the bottom of the tent as shown below. How many feet long, R, is the rope?

Answer 1

Length of Simon's tent = 6 feet

Distance from the bottom of the tent to the tent's base = 8 feet

Let the length of rope be R.

The tent and the rope forms a right angle triangle where the rope is the hypotenuse.

We know that :

`\color{hotpink} \tt{hypotenuse}^(2) \color{plum}= {base}^(2) + {height}^(2)`

Which means :

`= \tt {R}^(2) = {6}^(2) + {8}^(2)`

`=\tt {R}^(2) = 36 + 64`

`= \tt {R}^(2) = 100`

`=\tt R = √(100)`

`\hookrightarrow\color{plum}\tt \bold{R = 10 \: feet}`

Thus, the hypotenuse of this triangle = 10 feet

▪︎Therefore, the length of the rope = 10 feet