Question

$△$ABC is drawn with the length of side AB being 6.5 cm. If $\angle$A is 20${}^{\circ }$ and $\angle$C is 130${}^{\circ }$, then find the length of the side AC.

Answer 1

Here we are given the measures $\angle$A and $\angle$C.

We know that the sum of all the angles of a triangle is 180${}^{\circ }$. Hence we can find the measure of angle B.

$\angle$B = 180${}^{\circ }$ - ( $\angle$A + $\angle$C ) = 180${}^{\circ }$ - ( 20${}^{\circ }$ + 130${}^{\circ }$ ) = 30${}^{\circ }$ (1 marks)

Now, we have the following:

Length of side AB = 6.5 cm, measure of angle A = 20${}^{\circ }$ and measure of angle B = 30${}^{\circ }$

With these information in hand, it is possible to construct a triangle, as explained below.

Step 1:
Draw the base line AB of the length 6.5 cm. (0.5 marks)

Step 2:
Measure the angle A with your protractor. Make a mark at 20 degrees and draw a line from A passing through the mark. (0.5 marks)

Step 3:
Measure the angle B with your protractor. Make a mark at 30 degrees and draw a line from B passing through the mark. (0.5 marks)

Step 4:
Name the point of intersection of these two lines as C and the $△$ABC is complete, as shown below.

Now, from the above construction, we see that the length of side AC is 4.2 cm. (0.5 marks)