Question

How do I solve this? Not really getting at how and where the ropes are meeting.

Farmer Goldie McDonald is planning to lay a water pipe through a small bill. She needs to determine the length of pipe needed. From a point off to the side of the hill on level ground, she runs one rope to the pipe's entry point and a second rope to the exit point. The first rope measures 14.5 meters and the second is 11.2 meters. The two ropes meet at an angle of 58 degrees. What is the length of pipe needed? At what angle with the first rope should the pipe be drilled so that it comes out at the correct exit point?

Answer 1

This problem involves using trigonometry to find the length of the water pipe and the angle it should be drilled.

First, draw a diagram of the situation:

In this diagram, point A represents the location on level ground where the two ropes meet, point B represents the entry point of the pipe, point C represents the exit point of the pipe, and a, b, and c represent the lengths of the sides opposite to the angles A, B, and C, respectively.

We are given the lengths of the two ropes, 14.5 meters, and 11.2 meters, and the angle between them, 58 degrees. We can use the law of cosines to find the length of the water pipe:

c^2 = a^2 + b^2 - 2ab cos(C)

c^2 = (14.5)^2 + (11.2)^2 - 2(14.5)(11.2) cos(58)

c^2 = 211.29

c = 14.53 meters (rounded to two decimal places)

So the length of the water pipe needed is approximately 14.53 meters.

To find the angle with the first rope at which the pipe should be drilled, we can use the law of sines:

sin(A)/a = sin(C)/c

sin(A) = (a/c) sin(C)

sin(A) = (14.5/14.53) sin(58)

sin(A) = 0.984

A = sin^-1(0.984)

A = 80.83 degrees (rounded to two decimal places)

So the angle with the first rope at which the pipe should be drilled is approximately 80.83 degrees.

Explanation: