Let's start by drawing a diagram to visualize the situation:
We can start by using trigonometry to find the height of the pole. We know that the first cable makes an angle of 80° with the ground, so the angle between the cable and the pole is 10° (since the two angles add up to 90°). We can set up a ratio:
tan 10° = height of pole / distance from bottom of pole to where first cable is attached
tan 10° = h / 7
h = 7 tan 10°
h ≈ 1.23 m
Now we can use the height of the pole and the distance from the second cable to the pole to find the angle between the second cable and the ground. Let's call this angle x. We can set up another ratio:
tan x = height of pole / distance from second cable to pole
tan x = 1.23 / (3 * 7)
tan x ≈ 0.0583
To find the angle x, we need to take the inverse tangent of 0.0583:
x = tan⁻¹ 0.0583
x ≈ 3.33°
Therefore, the second cable makes an angle of approximately 3° with the ground.
A telephone pole is secured with two cables. The first cable is attached to the top of the pole and makes an
angle of 80° with the ground. The cable is secured to the ground 7 m from the bottom of the pole. The second
cable is attached to the top of the pole and secured to the ground three times as far from the pole as the first
cable is, on the same side of the pole. Determine the angle the second cable makes with the ground, to the
nearest degree.
1 answer
1 answer