Oblique Triangles

AB is a line 652 feet long on one bank of a stream, and C is a point on the opposite bank. A = 53° 18', and B = 48° 36'. Find the width of the stream from C to AB.

In a triangle ABC, a = 700 feet, B = 73° 48', and C = 37° 21'. If M is the middle point of BC find the length of AM, and the angles BAM and MAC

The sides of a quadrilateral in order are 763.83, 721.75, 547.12, and 593.21, and the angle between the first two sides is 53° 13' 12". Find the other three angles.

(Hint)-You know the sides of the quadrilateral ABCD and the angle at B. You can solve triangle ABC. Then you know all the sides of triangle ACD, so you can find its angles.

A and B are two points on opposite sides of a body of water, and soundings are to be taken in the line AB at points one quarter, one half, and three quarters of the distance from A to B. On the shore a line AC 1200 feet long is measured, and angles BAC = 63° 19' and ACB = 78° 43'. What angles must be turned off from CA at C in order to line up the boat from which the soundings are made at the proper points on AB?

(Hint)- First determine the distance AB using the law of sines. Then for each of the proper positions of the boat P, you know two sides and the included angle of the triangle PAC, so you can determine the needed angle using the law of cosines.

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