Question

BRO MY MATH TEACHER IS ON TO ME SOMEONE HELP A family camping in a national forest builds a temporary shelter with a tarp and a 6-foot pole. The bottom of the pole is even with the ground, and one corner is staked 10 feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole?

Answer 1

To find the slope of the tarp, we can use the concept of rise over run, which is the ratio of the vertical change (the rise) to the horizontal change (the run). In this case, the rise is the distance from the corner of the tarp to the top of the pole, and the run is the distance from the corner of the tarp to the bottom of the pole.

We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle formed by the corner of the tarp, the bottom of the pole and the top of the pole.

The length of the hypotenuse is the distance from the corner of the tarp to the top of the pole and the length of the adjacent side is the distance from the corner of the tarp to the bottom of the pole.

We know that:

adjacent side = 10 ft

Hypotenuse = h

Applying the Pythagorean theorem:

h^2 = 10^2 + 6^2

h = √(10^2 + 6^2)

h = √(100 + 36) = √136 = 11.66 ft

Now we can calculate the slope:

slope = rise/run = (h-10) / 6

slope = (11.66-10) / 6 = 1.66/6 = 0.277

So the slope of the tarp from the corner to the top of the pole is 0.277 or approximately 0.28.