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Alban · Answer 1 · 2023-08-05T07:53:14+0000

We are given a diagram showing a tower and a wire to be attached from the ground to the top of the tower. What we have is a non right angled triangle.

We shall start by constructing a few lines to determine the measure of the other angles.

We can see that a line drawn parallel to the ground from the bottom of the hill (yellow line) would intersect the upward rise of the hill. This would give rise to a corresponding angle measuring 57 degrees.

Note also that the angle opposite the one indicated (which is within the triangle is also 57 degrees (opposite angles are equal).

Also, observe that the line constructed (yellow line) is perpendicular to the tower which in effect forms a 90 degree angle. The angle at the right side of the triangle therefore is (90 + 57) 147 degrees.

Hence all three angles in the triangle would be;

$\angle30\degree,\angle147\degree,\angle3\degree$

We can now refine the triangle to look like the one shown below;

The side length marked x is the length of the guy-wire.

To calculate x, we shall use the sine formula which is;

$(a)/(\sin A)=(b)/(\sin B)$

Where our variables are;

$\begin{gathered} a=175,\sin A=3\degree \\ b=x,\sin B=147\degree \end{gathered}$

We shall now substitute for the given values and we'll have;

$(175)/(\sin3)=(x)/(\sin 147)$

We cross multiply this to become;

$(175*\sin 147)/(\sin 3)=x$