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:

c^{2} = a^{2} + b^{2}, 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.