# Using the Laws Related to Solving Oblique Triangles

Solving oblique triangles:

The trigonometry of oblique triangles is not as simple as that of right triangles, but there are two theorems of geometry that give useful laws of trigonometry. These are called the "law of cosines" and the "law of sines." There are other "laws" that used to be used, but since the common use of calculators, these two laws are enough. Apply these laws to the following questions.

Problems:

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

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

3. Three circles of radii 3, 4, and 5 touch each other externally. Find the angles of the triangle formed by joining their centers.

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Problems

1. 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.

C

A D B

Mathematically, we need to find CD, the distance from C to D.

Firstly, we find angle C = 180-( A+B)

C = 180-(53° 18'+ 48° 36')

C = 78° 6' degrees

We will use the law of sines:

sin A

________________________________________a = sin B

________________________________________b = sin C

________________________________________c

Now we use the ...

#### Solution Summary

Finding lengths of sides of a triangle using sine and cosine are provided.