How do I find the distance...?

Question

How do I find the distance between two lines running away from each other at a 30 deg angle for 200 meters? I mostly just need the answer since I'm not in trig anyway... but it would be nice to know how too.

This is assuming that the other angles are 60 and 90 degrees.

Answer 1

Well the first thing you always do with word problems is to draw a picture, which will be a triangle. Since you don't know if it will be right-angle, you will need the law of cosines to solve this. a^2 = b^2+c^2-2(b)(c)cos A. It's been a while since I've used it, but I believe the answer is 103.53 feet. What do you need to know this for? If it's for another class, you should probably figure it out yourself to be sure, because I might be wrong.

Answer 2

30-60-90 degres is a right Triangle

At the vertex of the 30 degrees angle are two sides. one is the Hypotenuse and the adjacent side. The side directly across from the 30 degree angle is the opposite side.

I am not sure of the question. do you wish to know the distance of both the opposite and adjacent side ? Which side does the 200 meters ?
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Let

o = Opposite side

a = adjacent side

h = hypotenuse

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h = 200

cosθ = a / h

cos 30° = a / 200

200cos30° = 200(a/200)

200(0.866025404) = a

173.2050808 = a

The answer is: a = 173.2 meters rounded to one decimal place.

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a = 200

cosθ a/h

cos30° = 200/h

hcos30° = h(200/h)

hcos30° = 200

hcos30° / cos30° = 200/ cos30°

h = 200/cos30°

h = 200 / 8.66025404

h = 230.9401077

h = 230.9 meters rounded to one decimal place.

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200 = opoposite side

find the Hypotenuse

sinθ o/h

sin30° = 200/h

hsin30° = h(200/h)

hsin30° = 200

hsin30° / sin30° = 200 / sin30°

h = 200 /sin30°

h = 200 / 0.5

h = 400

The answer is h = 400 meters

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I was not sure where to place the 200 meters

Once you have the answer of two of the sides solved, apply Phthagorean Theorem c² = a² + b² to obtain the third side.

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Answer 3

The two lines form an isosceles triangle, with a length of 200,
The base angle is congruent (property of isosceles triangle)
180 - 30 = 150/2 = 75.

If you divide the isosceles triangle in 1/2, then you come up with a right triangle. The angles of the triangle are 90, 75, and 15 (30/2, because it's 1/2 of the original angle)

Using sin angle = opposite/hypotenuse
Sin 15 = opposite/200
0.2588 = opposite/200
51.7638 = opposite

Since this is 1/2 of the original length
51.7638 x 2 = 103.53 (the distance between the two lines)

Answer 4

Your problem conforms to an isosceles triangle 200 meters on a side, base angles(opposite the 200 meter sides) are each 75 degrees, and apex angle 30. You're looking for the base length.

The bisector of the apex angle forms 2 right triangles where you can use the sine function to determine the base: Half the base / 200 = sine 15

the base/400 = sine 15. Therefore the base =
400 sin 15 = 103.5

Answer 5

Your hypothesis is wrong.
You can't have a isoscel triangle with an angle of 90 degrees unless this angle is situated between the two equal lines.

Answer 6

as you tell in additional details that to assume the other angles as 30 and 60 then i must say that the two lines cannot run 200m each , so total of two lines run will be 200m
if they both run 200m each then other angles can not be 30 60 it should be 75,75
so plz give that detailwhether total is 200m or not?