Question

A triangle is constructed such that one of its side 8 cm, another side is of length 5.5 cm and the angle opposite to the side of length 5.5 cm is 40⁰. This construction results in the formation of two triangles. Let us call the third vertex of the smaller triangle as C1 and the third vertex of the bigger triangle as C2, as shown in the image below.

Then find the value of (x + y).

Answer 1

Step 1: Draw the base line AB of the length 8 cm.

Step 2: Measure ∠A with your protractor. Make a mark at 40⁰ and draw a line from A passing through the mark.

Now, we must locate C. It should be 5.5 cm from B and also should be on the upper line, in order to form the required triangle. All points at a distance of 5.5 cm from B are on the circle centred at B of radius 5.5 cm. Thus, we have the next step.

Step 3: Draw a circle with centre at B and radius 5.5 cm. This circle cuts the line through A at two points.

Name the third vertex of the smaller triangle as C1 and the third vertex of the bigger triangle as C2.

Now, from the above construction we see that ∠AC1B = 110⁰ and ∠AC2B = 70⁰.

i.e., x = 110⁰ and y = 70⁰

Then, x + y = 110⁰ + 70⁰ = 180⁰.