In triangle ABC, find <A to the nearest tength of a degree is m<B=95 degrees , b=15.4, a=8.0
SinA/8.0 = sin 95º/15.4
solve for angle A
(I got 31.2º)
A park ranger at point A sights a redwood tree at point B at an angle 23 degrees from a fire tower at point C, From the fire tower, the Angle between the ranger and the tree is 123 degrees. If the ranger at point A is 2.3 miles from the fire tower at point C, how far is it from the ranger to the redwood tree at point B?
To find angle A in triangle ABC, 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.
In this case, we know that side a has a length of 8.0 units and is opposite to angle A. We also know that side b has a length of 15.4 units and is opposite to angle B.
Using the Law of Sines, we can set up the following ratio:
sin(A) / a = sin(B) / b
Let's substitute the known values into this equation:
sin(A) / 8.0 = sin(95) / 15.4
Now, let's solve for sin(A):
sin(A) = (8.0 * sin(95)) / 15.4
Using a calculator, we find that sin(A) ≈ 0.825563.
To find angle A, we can use the inverse sine (sin^-1) function:
A = sin^-1(0.825563)
Using a calculator, we find that angle A is approximately equal to 57.22 degrees.
Therefore, angle A is approximately 57.22 degrees to the nearest tenth of a degree.