This week in math, I learned how to solve an isosceles triangle, an isosceles triangle is a triangle with two equal sides. 

Example 1: 

First, we will start by writing SOH CAH TOA on the top of our page. For this question we will be finding the missing side, BC, of this isosceles triangle. We must first start by drawing a line down the middle to make it a right triangle. Because the triangle is isosceles the line will create two identical triangles with an A angle of 40 degrees each. We will now label the sides, the longest side of our triangle will always be the hypotenuse, the side opposite our given angle is the opposite side, and the side we have left is the adjacent. In this equation we will be solving for the opposite. To find the opposite of this triangle we will look at our SOH CAH TOA and use SOH, sine= . Our angle is Sine 40 so we will write our equation like, sine40= . We must now get O all alone, so to do this we will multiply sine= by 20 on either side of the equation. Now we are left with . is 12.9, but we must remember that 12.9 is only one half of the side we were trying to solve, so we must multiply it by 2, which gives us 25.7. So we now know that the side BC is 25.7cm. 

 

Example 2:  

For this triangle we are going to solve the missing sides and angles. We start out by knowing that angle B and angle C are both 22 degrees and sides AB and AC are 42cm, we must now solve for side BC. To find side BC we will first write SOH CAH TOA at the top of our page and draw a line down the middle of our triangle. Now by looking at the triangle we can see that the side opposite of 22 degrees is the line down the middle, making it the opposite side, the 42cm side will be the hypotenuse, and the side we are currently solving for is the adjacent. By looking at SOH CAH TOA we can determine that we will be using CAH, cosine= . Our equation will look like this, cosine= because we are solving for side a. Now we’re going to multiply both sides of the equation by 42 to get a alone, . We get the answer 38.9, but because we’re finding the side BC we need to multiply it by two making our final answer 77.9cm. Now because we are solving the whole triangle we must find angle A, to do this we can add angle B and angle C together, now because every triangle is equal to 180 degrees we can subtract 44 from 180 to give us the missing angle, . Angle A is 136 degrees.