Question

A 10 ft. tent pole has a support rope that extends from the top of the pole to the ground. The rope and the ground form a 30 degree angle. How long is the rope, rounded to the nearest tenth place?

Answer 1

So you have a pole that is 10 feet tall that has a rope that goes from the top to the ground, the rope being 30 degrees to the ground... You can draw a right triangle using these dimensions. Now that you have a triangle, you look at where your 30degree angle is related to the side whose length you know and the side whose length you wish to find. The side you know is opposite from the 30 degrees while the side you want to find is the hypotenuse, for it goes down at an angle. You will use the opposite and hypotenuse sides, so, according to SOH CAH TOA, you will be using sin.

`(opposite)/(hypotenuse)=sin\theta,\theta=30,opposite=10,hypotenuse=?`
plug in those values and solve for your hypotenuse.
The easiest way to do this is if you knew the identities for special right triangles like the 30 60 90 triangles or the 45 45 90 triangles, but I showed you how to solve for your sides even if they're not special

Answer 2

Answer: 20 feet.

Explanation:

From the given information, it is clear that the tent is vertical to the ground .

Therefore, they altogether make a right triangle with hypotenuse (h) and angle of elevation
`30^(\circ)`.

By trigonometry,

`\sin\ x=\frac{\text{side opposite to the x}}{\text{hypotenuse}}\\\Rightarrow\ \sin(30^(\circ))=(10)/(h)\\\Rightarrow\ (1)/(2)=(10)/(h)\\\\\Rightarrow\ h=20`

Hence, the length of the rope (h)=20 feet.