An h = 135-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. a guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. find the shortest length of wire needed. (round your answer to the nearest foot.)

By applying the Law of Cosines, the shortest distance of the needed wire, to the nearest foot, is: 171 ft.

Recall:

The given scenario has been sketched in the diagram showing the tower that is located on the side of a mountain alongside other information that are provided.

The shortest distance is represented as x.

To find x, we would apply the law of Cosines,  .

d = 55 ft

f = 135 ft

e = x

Therefore, by applying the Law of Cosines, the shortest distance of the needed wire, to the nearest foot, is: 171 ft.

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171 foot

Step-by-step explanation:

We are given that

Height of tower=135 ft

AC=55 ft

Let x be the length of shortest length of wire.

The angle of inclination of mountain with horizontal =

The angle between sides AB and BC=

Exterior angle is equal to sum interior angles of a triangle on the opposite sides .

We have to find the value of x.

We know that law of cosine

Substitute the values in the given formula we get

Hence, the length of wire needed=171 foot

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl