Trig question?

Question

First of all I will type the question and then explain what my problem is.

A 41 m guy wire is attached to the top of a 34.6 m antenna and to a point on the ground. How far is the point on the ground from the base of the antenna, and what angle does the guy wire make with the ground?

I found that the point from the ground to the base of the antenna is 22 m, which according to my book is correct. Now, I know there is a 90 degree angle in there, but I'm confused as to how to find the other angles since no other angles were given. Can someone please explain to me how to do this?

Answer 1

Yes.

If you have the length of the wires, you can find angles.

If Sin x = opposite length/hypotenuse length, then just divide the lengths, and figure out what angle has a sin of whatever that value is.

If you have a graphing calculator, just press sin-1 for that number.

In your case, it'd be sin-1(34.6/41) = whatever.

Answer 2

Using sine and tangent function, you can get the point from the ground to the base of the antenna. The answer is 22m. Here's how.

sin x = 34.6 / 41
x or the angle the wire makes with the ground = arcsin (34.6 / 41) = 57.55 deg

To get the distance from the ground to the base of antenna, use tangent function:

tan 57.55 = 34.6 / D where D is the distance from ground of the wire to the antenna

D = 34.6 / tan (57.55) = 22

The other angle now that the guy wire makes with respect to the antenna is 90 deg - 57.55 deg = 32.45 deg

The 90 deg is the angle the antenna makes with the ground

Answer 3

H - Height.
G - Ground.
S - Slope.

H² + G² = S²
G² = S² - H²
G = √(S² - H²)
G = √(41² - 34∙6²)
G = √483∙84
G = ± 21∙996 363 34...m
G ≈ 22m.

You can use the Sine rule here.
Sin h/ H = Sin g/ G = Sin s/ S
Using:
Sin g/ G = Sin s/ S
Sin g = G Sin s/ S
Sin g = (21∙996 363 34...) * Sin 90°/ 41
Sin g = (21∙996 363 34...) * 1/ 41
Sin g = 0∙536 496 666...
g = Sin^-1 (0∙536 496 666...)
g = 32∙445 4687...°
g ≈ 32∙45°

h = 90° - 32∙445 4687...°
h = 57∙554 5313...
h ≈ 57∙55°

Answer 4

Remember all triangles have 180 degrees and a(sq) + b(sq) = c(sq). The base of the antenna and the ground form the 90 degree angle. You should be able to use your trig functions (sin, cos, tan) whichever you find easiest to determine the angle of the wire.

Answer 5

Certainly, this is why trigonometry was discovered.

34.6 m hieght and 41 m = hypotenuse 22m = a side

sin = 34.6/41 = 57.554531 is the angle opposite the hypotenuse

90 is the right angle

90 - 57.554531 = 32.445469

angles are 32.4454, 57.55453 and 90

Ta da