Camping Stakes
April 9th, 2010 at 14:09Trig help....??
I don't understand the picture for it or the following problem:
Jim and his friends are going camping in the tent. Each side of the tent forms a right angle with the ground. The tops of two ropes are attached to each side of the tent 8 feet above the ground. The other two ends of the two ropes are attached to stakes on the ground.
If the rope is 12 feet long, what angle does it make with the level ground; And what is the distance between the bottom of the tent and each stake??
Help Please
You have to draw the picture in your head, basically it'll end up looking like an average right triangle.
The opposite leg is 8 feet. This is given when they say that the ropes are attached 8 feet above the ground.
The hypotenuse is 12 feet. This is given when they say that the rope is 12 feet long.
To find the measure of theta (the angle with the level ground), you have to determine which trig property uses both the hypotenuse and the opposite leg.
Since sin x = opposite / hypotenuse , this is the one you should use.
sin x = opposite / hypotenuse
sin x = 8 / 12
sin x = 2 / 3
sin x = .6666666
Take sin^-1 of each side to find the angle measurement.
sin^-1 sin x = sin^-1 .6666666
x = 41.8103 degrees
That's the angle it makes with the ground.
Now, to find the distance between the bottom of the tent and each stake, you can use the Pythagorean Theorem.--->
a^2 + b^2 = c^2
In this equation, a and b refer to legs of the triangle and c is the hypotenuse. So, all you have to do is plug in your values and simplify.
a^2 + b^2 = c^2
a^2 + 8^2 = 12^2
a^2 = 12^2 - 8^2
a^2 = 144 - 64
a^2 = 80
Take the square root of each side.--->
sqrt(a^2) = sqrt(80)
a = sqrt(5) * sqrt(16)
a = sqrt(5) * 4
a = 4*sqrt(5) feet
That is your distance from the tent to each stake.
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Tags: backpacking, Camping, diy, rope, stakes