## 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.

Solution:

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

## Monday, April 29, 2013

### Word Problem - Age Problem

Category: Algebra

"Published in Newark, California, USA"

Six years ago, Rosario was 4 times as old as her daughter. Ten years from now, she will be only twice as old as her
daughter. How old are they now?

Solution:

The given word problem is about age problem where you   need to solve for the age of a person or people. Let's analyze the given word problem above as follows:

Let         x = be the present age of Rosario
y = be the present age of Rosario's daughter
x - 6 = be the age of Rosario six years ago
y - 6 = be the age of Rosario's daughter six years ago
x + 10 = be the age of Rosario ten years from now
y + 10 = be the age of Rosario's daughter ten years from now.

If the first statement says, "Six years ago, Rosario was 4 times as old as her daughter." then the first working equation will be

If the second statement says, "Ten years from now, she will be only twice as old as her daughter." then the second working equation will be

Next, equate the two working equations in order to solve the age of Rosario's daughter as follows

Substitute the value of y to either of the two working equations in order to solve for the age of Rosario as follows

Therefore, in present time, Rosario is 38 years old while her daughter is 14 years old.

## Saturday, April 27, 2013

### Solving Trigonometric Equations, 4

Category: Trigonometry, Algebra

"Published in Suisun City, California, USA"

Find the value of x for

Solution:

Consider the given equation above

By looking at the equation above, the factors of 4sin x cos x are 2sin x and 2cos x while the factors of -1 are 1 and -1. Since there are 2sin x, -2cos x, and -1 in the equation above, then we can rewrite the above equation as follows

Equate each factor to zero and solve for the value of x.

If
then

Since the value of sine is positive at 1st and 2nd Quadrant, then

where n is the number of revolutions.

If
then

Since the value of cosine is negative at 2nd and 3rd Quadrant, then

where n is the number of revolutions.