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Trigonometry
Solving right triangles

To solve a triangle is equivalent to find unknown parts in terms of known parts.

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle.

Solving right triangles when we know two sides.
1. The Pythagorean theorem will give us the unknown side.
2. Use a sine, cosine, or tangent to determine an unknown angle.
3. Remember that the sum of the three angles equals 180º to find the third missing angle.

Solve the triangle showed:

1. Using the Pythagorean theorem:
c2 = a2 + b2, por tanto b 2 = c 2 - a 2 ;
b 2 = 5 2 - 3 2 ; b 2 = 25 - 9 ; b 2 = 16 ; b = 4.

2. Using the sine:
senA=3/5, then A=arcsen(3/5) ; A= 36'87º.

3. A+B+C=180º and C=90º, then B=180º -90º-36'87º ; B= 53'13º

So that: The sides are 3, 4 and 5, and the angles are 90º, 36'87º y 53'13º.

Solve the triangle
 = = =3 = =6 =
Note: Express the angles using only degrees (25º30' = 25.5º). Round off using only two figures.