A cable 19 m long runs from the top of a utility pole to a point on the ground 10 m from the base of the pole. How tall is the u
1 answer:
Answer:
16.2 m
Step-by-step explanation:
First, we can draw a picture. The cable goes from the top of the pole to the ground (with the pole on the right in my drawing), and the point on the ground is 10 m away from the base of the pole. This forms a right triangle, with the right angle being between the 10 m distance and the pole itself. We can then apply the Pythagorean Theorem, so
a²+b²=c², with c being the side opposite the right angle (the cable), getting us
10²+(length of pole)² = 19²
19²-10²=(length of pole)²
= 261
square root both sides to isolate the length of the pole
length of pole ≈ 16.2 m
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The length of the support wire on the pole is 27 feet
<h3>How to determine the length of the support?</h3>The given parameters are:
- Distance from the base, b = 10 feet
- Angle with the ground, x = 68 degrees
The length (L) of the support wire is then calculated using the following cosine function
cos(x) = b/L
This gives
cos(68) = 10/L
Make L the subject
L = 10/cos(68)
Evaluate
L = 27
Hence, the length of the support wire is 27 feet
Read more about triangles at:
#SPJ1
