How to find all angles and all sides

Today in Maths I have been working on explaining how to the the Maths calculation of How to find all angles and all sides. This question was based on the test our class had to the day prior to making this post. Hope you enjoy this post,

S              C               T
O/H          A/H           O/A
We are using sign because we are given the Opposite and the Hypotenuse.

Sin = OPP/HYP
Sin = 12/17
Which means we dived 12 by 17=0.7058
Then on the calculator we press (shift, sin) which now means sin-1 when we put 0.7058 in we get an answer of 44.894. This means the first angle is 44.894 degrees.



               

To find angle number we know that all angles in a triangle equal 180 we have two angles already discovered which are 90 degrees(because it's a right angle) and the angle we discovered just before 44.894. We can add 90 degrees+44.894 which = 134.894 degrees. Then we do 180 degrees - 134.894 degrees= 45.106 which means the angle number two equals 45.106 degrees.

Now we need to find the length of the final side, side B. To find length of side B we can can use a^2 + b^2 = c^2. 12^2 + b^2 = 17^2, 144 + b^2 = 289. Change side change sign. 289-144= 145. Square root of 145 = 12.04=Side B.














Angle Check:
90 + 44.894 + 45.106= 180
All angles are correct.

Side Check:
12^2 + 12.04^2=17^2
144 + 145 = 289.
All sides are correct.