A telephone is anchored to the ground by a long cable called a guy wire, at a point 5 meters from the base of the pole, the wire makes an angle of 72.5 degrees with the horizontal. What is the length of the guy wire?
HELP ASAP! I forgot how to compute for this (Pythagorean Theorem) D:
We don't need Pythagorus, we need trig.
let the height be h
h/5 = tan 72.5°
h = 5tan 72.5 = appr 15.858 m
Thank you so much!
A telephone pole anchored to the ground by a cable called guy wire at a point of 5m from the base of the pole. The wire make an angle of 72.5 with the horizontal. WHAT IS THE LENGTH OF THE GUY WIRE AND WHAT IS THE HEIGHT OF THE POLE WHERE THE GUY WIRE IS ATTACHED TO? THANKS!
No worries! I can help you with that. To find the length of the guy wire, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the guy wire, the ground, and the pole form a right-angled triangle. The guy wire is the hypotenuse, and the distance from the base of the pole to the point where the wire makes an angle is one of the shorter sides.
Let's label the length of the guy wire as "c" and the distance from the base of the pole to the point where the wire makes an angle as "a." The angle between the guy wire and the horizontal is given as 72.5 degrees.
Using trigonometry, we can determine that the adjacent side can be represented as "a = 5 meters." The cosine function relates the adjacent and hypotenuse sides: cos(θ) = adjacent / hypotenuse.
Therefore, cos(72.5) = 5 / c.
To find the length of the guy wire, we can rearrange this equation as follows:
c = 5 / cos(72.5).
Now we can calculate it:
c = 5 / cos(72.5)
c ≈ 5 / 0.3140 ≈ 15.92 meters.
So, the length of the guy wire is approximately 15.92 meters.