to find the distance AB across a river, a distance BC= 309m is laid off on one side of the river. It is found that B= 105.4 degrees and C= 12.2 degrees. Find AB

To find the distance AB across a river, a distance BC= 309m is laid off on one side of the river. It is found that /_B= 105.4 degrees and /_C = 12.2 degrees. Find AB

If angle B is 105.4º, distance AB is not normal to the banks of the river, assuming the banks are parallel.

With the given information, distance AB may be found using the Law oof Sines. WIth /_A being 180 - 105.4 - 12.2 = 62.4º, AB/sin(12.2) = 308/sin(62.4).

Solve for AB.

AB = 308sin(62.4)/sin(12.2) ≈ 545.7m

To find the value of AB, we can use the Law of Sines. This law states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant across the triangle. In this case, we will use the sine of angle B and angle A.

First, we need to find angle A. To do this, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, angle A = 180 - angle B - angle C = 180 - 105.4 - 12.2 = 62.4 degrees.

Now that we know angle A, we can set up the Law of Sines equation: AB/sin(angle B) = BC/sin(angle A).

Plugging in the known values, we have: AB/sin(105.4) = 309/sin(62.4).

To solve for AB, we can cross-multiply and then isolate AB: AB = (sin(105.4) / sin(62.4)) * 309.

Using a calculator, we can find the sine values and calculate the final answer for AB.

To find AB, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

We have the following information:

BC = 309m
B = 105.4 degrees
C = 12.2 degrees

To find angle A, we can use the fact that the sum of the angles in a triangle is 180 degrees:

A = 180 - B - C
A = 180 - 105.4 - 12.2
A = 62.4 degrees

Now we can use the Law of Sines to find AB:

AB / sin(C) = BC / sin(A)

Plugging in the values we know:

AB / sin(12.2) = 309 / sin(62.4)

Now we can solve for AB:

AB = (309 * sin(12.2)) / sin(62.4)

Using a calculator to evaluate the sine values, we have:

AB = (309 * 0.211) / 0.888

AB ≈ 73.8m

Therefore, the distance AB across the river is approximately 73.8m.