Q: A 4m flag pole is not standing up straight. There is a wire attached to the top of the pole and anchored in the ground. The wire is 4.17m long. The wire makes a 68 degree angle with the ground. What angle does the flag pole make with the wire?

Question

Q: A 4m flag pole is not standing up straight. There is a wire attached to the top of the pole and anchored in the ground. The wire is 4.17m long. The wire makes a 68 degree angle with the ground. What angle does the flag pole make with the wire?

Show all the work please and the answer because I don't get this question at all!!!

Answer 1

try drawing a picture

you can find the height of the top of the pole ... 4.17m sin(68º)

use the height and the length of the pole to find the angle of the pole
... cos(Θ) = height / length

Answer 2

Could you please also put the answer up as well so that I can check my work?

Thanks

Answer 3

just realized this is supposed to be sine/cosine law based

law of sines ... sin(Θ) / 4.17 = sin(68º) / 4

Answer 4

So, if sine law is used then won't there be 2 answers because of the ambiguous case of the sine law.

Also if the angle that we are looking for is between the wire and the pole, when it is drawn it will be where the pole and wire meet correct?

Answer 5

Also how would you use the cosine law because the 3rd side length isn't given and we don't know if it is a right triangle or not so we can't use the Pythagorean Theorem.

Answer 6

use the law of sines to find the angle opposite the wire (pole/ground)

the 3rd angle of the triangle (between the wire and the pole)
... is just 180º , minus the other two angles (68º and pole/ground)

Answer 7

To find the angle that the flag pole makes with the wire, we can use trigonometry.

First, let's label the information given:

Height of the flag pole (opposite side) = 4 meters
Length of the wire (hypotenuse) = 4.17 meters
Angle between the wire and the ground = 68 degrees

We need to find the angle between the flag pole and the wire (adjacent side). Let's call this angle θ.

Now, we can use the trigonometric function tangent (tan) to solve for θ:

tan(θ) = Opposite side / Adjacent side

In this case, tan(θ) = 4 / Adjacent side

Now, we can calculate the adjacent side (Opposite side / tan(θ)):

Adjacent side = 4 / tan(θ)

To find θ, we need to take the inverse tangent (arctan) of the ratio of the opposite side to the adjacent side:

θ = arctan(4 / Adjacent side)

Substituting the value of the adjacent side, we get:

θ = arctan(4 / (4.17))

Now, we can calculate the value of θ using a calculator:

θ ≈ arctan(0.959))

θ ≈ 44.9 degrees

Therefore, the angle that the flag pole makes with the wire is approximately 44.9 degrees.