A 10-meter-long wire is attached to the top of a flagpole that is [tex]5\sqrt{3}[/tex] meters tall. What is the measure of the angle the wire makes with the ground?

A. 25 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees

Well there has to be a right angle in there somewhere as the pole must be perpendicular to the ground.
Using the sine rule: sinA/a = sinB/b where a = 10, A = 90, b = 5√3, B = B Re-arrange for B, B = arcsin (b(sinA)/a) B = arcsin(5√3(sin90)/10) B = 60 degrees.
Answer is C

Answered by jdpclarke | 2024-06-10

The student's question involves finding the measure of the angle that a wire makes with the ground when it is attached to the top of a flagpole.
To solve this problem, we can use trigonometry since we have a right triangle formed by the flagpole, the ground, and the wire.
The height of the flagpole is given as 5\sqrt{3 meters, and the length of the wire is 10 meters. Thus, we can use the tangent ratio, which is the opposite side over the adjacent side in a right triangle.
We can write the following equation using the tangent function (tan) for the angle θ (theta): tan(θ) = opposite side / adjacent side = 5\sqrt{3 / 5 = \sqrt{3.
When we look at the well-known angles and their tangent values, we find that tan(60) = \sqrt{3 . Therefore, the angle that the wire makes with the ground is 60 degrees (C).

Answered by AliciaAugello | 2024-06-24

To find the angle the wire makes with the ground, we can use the sine function. After calculations, we determine that the angle is 60 degrees. Therefore, the answer is C.
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Answered by jdpclarke | 2024-12-27