This week in math 10 we started our new unit on trigonometry. So far we have covered trigonometric ratios, how to use calculators for trigonometric ratios and calculating and measuring the sides and angles of right angled triangles. While all of these different concepts have been interesting to learn about, I believe the most important thing I learned was how to identify and name all the sides of right angled triangles. I believe that this concept was the most important concept I learned this past week because without knowing what side of the triangle is which, you are unable to determine the angles or what the lengths of the right angled triangles are.

Right angled triangles have three different sides, the hypotenuse, the opposite and the adjacent.

The Hypotenuse:

-The longest side

-Opposite of the right-angle

 

The Opposite:

-Opposite of the angle you’re looking for (reference angle)

-Opposite of the angle we know (reference angle)

 

The Adjacent:

-The side “left over”

-The side next to the right angle and the angle involved in the question (reference angle)

 

SOH CAH TOA

To calculate the unknown angle or side length of a right angled triangle a helpful trick to remember is SOH CAH TOA. These three mnemonic devices help remember the trig rules of sine, cosine and tangent.

SOH:

sine=opposite/hypotenuse

CAH:

cosine=adjacent/hypotenuse

TOA

tangent=opposite/adjacent

 

Finding the missing length:

In order to find the missing length of a right angled triangle, first you must label the sides of a triangle (which is the opposite, adjacent and the hypotenuse.) Once you have identified all the sides of the triangle, you need to determine which side you are looking for, which side is already known and what the reference angle is. Once you have determined all three things you can choose which equation is the appropriate one to use.

Once the ratios have been put into an equation, you just need to solve for x with the assistance of a calculator.

Finding the missing angle:

In order to find the missing angle of a right angled triangle first you must label the sides of a triangle (which is the opposite ,adjacent and the hypotenuse.) Once all the sides are labeled you need to determine which trig formula you will use based on what side lengths you already know.

Once the ratios have been put into the equation to solve for x the tangent will be inversed so that the answer will be the angle instead of the side length.