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Tuesday, April 30, 2013

Subtended Angle Problem

Category: Trigonometry

"Published in Newark, California, USA"

A vertical pole is 35 ft. high and stands on sloping ground. It is braced by a guy rope which extends from the top of the pole to a point on the ground 25 ft. from the foot of the pole. The pole subtends an angle of 30° at the point where the guy rope reaches the ground. Determine the length of the rope.


The given word problem is about subtended angle. Subtended angle is the angle formed by an object at a given external point. Slopping ground means that the ground is not horizontal and it is slanted or inclined. To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

The above figure forms an oblique triangle. Analyze further the figure, we have

Photo by Math Principles in Everyday Life

From the given items of an oblique triangle, use Sine Law in order to solve for angle A as follows

We know that the sum of the angles of a triangle is always equal to 180°. If we know the two angles of a triangle, then we can solve for the other angle as follows

Finally, use Sine Law again in order to solve for the length of a rope as follows