Question

For the following exercises, suppose that x2 = 25 + 36 − 60 cos(52) represents the relationship of three sides of a triangle and the cosine of an angle.

Draw the triangle.

Answer 1

The equation is given below,

x2 = 25 + 36 – 60cos(52)

 

The given equation can be re-written as follows:

x2 = (5)2 + (6)2 – 2(5)(6)cos(52)

 

The equation written above resembles to the Law of Cosines stated below:

a2 = b2 + c2 – 2bccosα

 

Therefore, it can be inferred from above that,

b = 5    c = 6    α = 52°

 

Where b and c are the adjacent sides of a triangle and α is the angle contained between them.

The following steps are to be followed to draw the required triangle.

 

Step 1: First, draw a line segment of length 5cm named AB as shown below,

 

Step 2: At one of the ends of the line segment, suppose A, draw a line at 52° to AB as shown below,

 

Step 3: Measure 6cm and cut it off from the line drawn in the previous step as shown below,

 

Step 4: The point at which the line is cut is marked C as shown below,

 

Step 5: Join points C and B as shown below,

 

Hence, the required triangle is obtained.