This week in math we finished up our trigonometry unit.

We did lots of work on word problems making sure we understood things such as angle of depression, elevation, and making sure we knew where to place the numbers that were given to us.

Here is an example:

Our first step of course is to draw out our right triangle.

Our next step is to fully analyze the word problem and start to pick out our angles and our sides.

In the word problem they tell are we have a flag pole which is 5ft high so of course we know where to place our 5 on our triangle which is going to be our vertical side. We are also given a shadow (3.2 ft)which the flag pole makes. When we look at a shadow in real life we see it straight on the ground so in a word problem whenever we see the word shadow it will be our horizontal side.

In this image I placed the sides and i also add the angle. I knew that the angle went there because in the word problem it’s asking up for the angle of elevation of the sun and the word elevation means the angle is at the bottom across from the right angle. X is our place holder since we are trying to figure out that angle.

In this final photo i solved the equation. The first thing i did was label our sides. 5 being our opposite side since it’s across from our angle and 3.2 being our adjacent side since our hypotenuse is always our longest side. The next step is to figure out which ratio we have to use to get the correct answer. Our options are Tangent, Sine, or Cosine. As you can see i chose tangent because we are given our opposite and adjacent sides. Next we plug our numbers into our equation which is shown on the left side of my image. Tan X= 5 over 3.2 (opposite over adjacent)

All we have left is to switch our equation around so we can plug the numbers into our calculator leaving our final answer to be X= 57.4 We need to put a dot over our equal sign to show that we rounded our answer.