SOLUTION: Can you please help me with this problem. I need to solve for the following angle. This question is from Algebra II, A Beka Book. The science club wants to find out the height of

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please help me with this problem. I need to solve for the following angle. This question is from Algebra II, A Beka Book. The science club wants to find out the height of       Log On


   

Question 86013: Can you please help me with this problem. I need to solve for the following angle. This question is from Algebra II, A Beka Book.
The science club wants to find out the height of the school's flagpole. They found that if the rope attached to the top of the pole was lengthened, it formed an angle of 60 degrees with the ground, 14 ft. from the base of the pole. What is the length of the pole?
Thank you so much for your help.
Found 2 solutions by tutor_paul, bucky:
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
The flagpole, rope and ground form a right triangle, with the rope being the hypoteneuse. Let x = height of the flagpole. You can write the following:
tan%2860%29=x%2F14
x=14%2Atan%2860%29
since tan(60)=sqrt(3), the final answer is:
highlight%2814sqrt%283%29%29
Good Luck,
tutor_paul@yahoo.com

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
A right triangle is formed in the problem you described. The right triangle has as its
hypotenuse, the length of the rope, and its two legs are: (1) the 14 ft distance from the base
of the pole to the point where the rope just touches the ground and (2) the height of the pole.
.
You know the 14 ft leg, and you need to find the other leg that is opposite the 60 degree
angle. The tangent is the function to use. Use the definition of the tangent which is
.
tan%28A%29+=+%28opp%2Fadj%29
.
where opp represents the side opposite the angle, and adj represents the side adjacent
to the 60 degree angle.
.
In this case you can substitute the known values to get:
.
tan%2860%29+=+opp%2F14
.
Multiplying both sides of this equation by 14 results in:
.
opp+=+14%2Atan%2860%29+=+14%2A%281.732050808%29+=+24.24871131
.
[Note that you can get tan(60) from your calculator by setting it to degrees mode,
entering 60, and pressing the "tan" key. If you do this correctly, your calculator
will give you the answer of 1.732050808.]
.
The answer of 24.24871121 indicates that the height of the flagpole (the side opposite the
60 degree angle) is approximately 24.25 feet which is about 24 feet 3 inches.
.
Another way you can do this is by recognizing that a 60 degree right triangle has sides
that are in the following proportions: the hypotenuse = 2, the side opposite the 60 degree
angle is sqrt%283%29 and the side adjacent to the 60 degree angle is 1. You can check
this with the Pythagorean theorem which will show that:
.
2%5E2+=+%28sqrt%283%29%29%5E2+%2B+1%5E2+=+3+%2B+1
.
Since you are involved with the side opposite and the side adjacent you can establish
the following proportion involving similar triangles:
.
%28standard%2Aside%2Aopposite%29%2F%28standard%2Aside%2Aadjacent%29+=+%28flagpole%29%2F14
.
But the standard side opposite is sqrt%283%29 and the standard side adjacent is 1.
Substituting these into the proportion results in:
.
sqrt%283%29%2F1+=+%28flagpole%29%2F14
.
You can solve this by multiplying both sides by 14 to get rid of the denominator of the
term containing "flagpole". When you do the equation becomes:
.
flagpole+=+14%2Asqrt%283%29
.
and if you use a calculator to multiply out the right side you again get:
.
flagpole+=+24.24871131
.
which also indicates that the flagpole is about 24.25 feet long.
.
Hope this helps you to understand the problem.