# Solving Right Triangles

### Austin Pittsley

## Using the Pythagorean Theorem

# Solving 45-45-90 Triangles

**GIVEN A LEG:**

If given a leg when solving a 45-45-90 triangle, you must know this ratio: x : x : x(square root)2. Since you are given a leg and x=x the two legs are the same. To find the hypotenuse you put the leg (or x) in front of the radical 2.

__GIVEN THE HYPOTENUSE:__

If given the hypotenuse when solving a 45-45-90 triangle, you still must know the same ratio as above.you must set the x(square root)2 equal to the leg x and divide by square root 2. The you have to multiply that by square root 2 over square root 2 to find your legs.

# Solving 30-60-90 Triangles

__ GIVEN A LEG: __If given a leg when solving a 30-60-90 triangle, you must know this ratio: x : x(square root) 3 : 2x. Since you are given a leg and you put the first leg in front of radical 3. To find the hypotenuse you multiply the first leg or x by 2.

** GIVEN THE HYPOTENUSE:**If given the hypotenuse when solving a 30-60-90 triangle, you still must know the same ratio as above.you must divide the hypotenuse by 2 to kind x.Then you put that leg or x in front the radical 3.

# Trigonometry: Using Sine, Cosine, and Tangent

__SINE:__ Opposite over hypotenuse

**COSINE:**** Adjacent over hypotenuse **

__TANGENT:__ Opposite over adjacent

Using all of these calculations you have to pay attention to the theta so you know what calculation to use.

# Trigonometry: How to Solve for Angle Measures

1. Figure out if you use SOH, CAH, or TOA

2. put variables in equation

3. Solve

# Work Cited

- Mathisfun.com
- Geometry Book
- Google Images