This week, I learnt how to solve any right angle triangle by only knowing 3 things about the triangle.

1st of all, it has to have a 90° angle, as it’s a right angle triangle.

2nd, you can know any 2 sides or angles and then you’ll be good to solve.

 

 

 

 

 

Once you have your triangle, the first thing to do is name all the sides based on the angle of reference. In this case, our angle of reference is the 32°, so we’ll name everything based on that.

 

 

 

 

 

The second step is to figure out what equation we need to use using SOH CAH TOA. In this case, since we have the the H already, we can easily solve for either the SOH or CAH. We’ll start of with SOH. Here is the equation:

 

 

 

 

 

The answer is ~218.86.

So now we know the length of O is 218.86cm.

 

 

 

 

 

Next, we can solve the 3rd angle by just using the rule that all angles in a triangle adds up to 180°. With a 90° angle and a 32° angle, we can figure out that the 3rd angle is 58°.

 

 

 

 

 

Finally, let’s solve for a.

To find a, we could use CAH or TOA, as we have all other information about the triangle already. We are going to use CAH because it’s easier. Here is the equation:

 

 

 

 

 

The answer is ~350.24

So now we know everything there is to know about the triangle.