Find the angle

[BMAD]

In a small community there are four households. The Abuleto Family, Boggs Family, and Carlos Family live are the corners of this community. The Douglas’s live between the Abuleto family and the Bogg’s family but not equidistant between them. There is a dirt path that runs directly from the back of Carlos family and Douglas families’ homes. This dirt path is straight. The neighborhood is surrounded by sidewalks that go to each adjacent house (straight line). The angle between the dirt path from Douglas to Carlos and the sidewalk for Bogg’s and Carlos is fifteen degrees. The distance of the sidewalk between Bogg’s and Carlos is sqrt(6) miles, while the distance between the Abuleto and Douglas families is only 1 mile. What is the angle between the sidewalks of the Abuleto family?

[TimeSpaceLightForce]

Let ABC = t and AC = x.

Then ADC = t + 15° and DCA = t - 15°.

The neighborhood is surrounded by sidewalks

that go to each adjacent house (straight line)

AB _/_AC or AB_/_BC

above ,the triangle is isoceles with BAC + t + t

if we divide BAC ..we have a right triangle with

90+t+t so t=45deg so BAC =90deg

[BMAD]

[bonanova]

There is not enough information to solve.

Proof:

Draw BC of length 6^.5.

From C, draw a ray R1 inclined 15^o.

From B, draw a ray R2 inclined at some angle in the first quadrant.

Where R2 intersects R1 (call it point D) proceed one unit further and place point A.

Draw AC.

Now you have the figure given in post #2.

Angle B is any first-quadrant angle.

Angle A depends on angle B; it has no discoverable value.

[TimeSpaceLightForce]

make a red line parallel to blue = 1mi

connect to B perpendicularly.

Measure green A angle: 67 deg

[TimeSpaceLightForce]

make a red line parallel to blue = 1mi @45deg

connect B to red 45deg.

Measure green A angle: 90 deg

or

make a red line parallel to blue = 1mi vertically

connect B to red vertically..

Measure green A angle: 56 deg

[BMAD]

Let ABC = t and AC = x.
Then ADC = t + 15° and DCA = t - 15°.

Edited May 4, 2013 by BMAD

[TimeSpaceLightForce]

deleted

Edited May 6, 2013 by TimeSpaceLightForce