how do I do this? expressing a function.?

Question

A guy wire (a type of support used for example, on radio antennas) is attached to the top of a 50 foot pole and stretched to a point that is d feet from the bottom of the pole. Express the angle of inclination as a function of d.

a=50ft
b=58.56ft
c=77ft

C=90 degrees

Thats what I have figured out. I just don't know how to express this as a function of d

Answer 1

The pole forms a right triangle. The angle of inclination is the angle between the ground and the wire.

Thinking about it visually, you know the angle, the adjacent leg (d) and the opposite leg (50).

Using the SOH-CAH-TOA mnemonic... since you have the opposite and adjacent legs, use TOA (tan = opposite/adjacent).

tan(angle) = opposite / adjacent
tan(angle) = 50 / d

To get the angle, take the arctan of both sides:
angle = arctan ( 50/d )

So the angle of inclination, expressed as a function of d, is:
angle = arctan ( 50 / d )

In your example, you said the hypotenuse was 77 feet and therefore the other leg (d) is 58.55766 feet.

Plug this into the formula and solve:
angle = arctan ( 50 / 58.55766 )
angle = arctan ( 0.85386 )
angle ≈ 40.5 degrees

Answer 2

okay first what we know:

The pole (side A) is 50 ft
The angle the pole is at is 90 degrees.

Pythagorus states A^2 + B^2 = C^2, but we only know 1 side.

We know trig ratios!

Cos X = Adjacent/Hypotenuse
Cos 90 = 50/Hyp
-0.448073616 = 50/Hyp
Hyp = Approx 111.59

50^2 + B^2 = 111.59^2
12452.3281 - 2500 = B^2
B = Approx 99.76

Now we know all lengths.

Tan X = Opp/Adj
Tan X = 50/99.76
X = I don't have a calculator to do this with :p

Answer 3

.....|\
50 |_\
......d

Let the angle be A. Then Tan A = 50/d and A= Arctan(50/d)

Answer 4

tanA = a/b
A = tan^-1(a/b)

In this case, b = d

A = tan^-1(50/58.56)
A = tan^-1(5000/5856)
A = tan^-1(625/732)

ANS : A = tan^-1(625/732)

the angle would be about 40.492