Question

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?

Answer 1

Draw a triangle and use the law of sines. The angle at B (between ranger and fire tower) is B = 180 - 23 - 123 = 34 degrees. You want the distance from A to B and that is related to angle C as follows:
AB distance/sin C = AC distance/sin B
AB distance = (sin C/sin B)*2.3 miles
= (sin 123/sin34)2.3 = 3.45 miles

Answer 2

a flagpole casts a shadow of 12m.the sun has an angle of elevation of 36. how tall is the flagpole?

Answer 3

since you know the height of the shadow and an angle, you can use a trig function to find the height of the flagpole, assuming that the triangle formed is a right triangle, unless you know the Law of Sines and the Law of Cosines.