Question

A triangle of sides AB = 2 cm, BC = 1.5 cm and AC = 1 cm is constructed. Then the measure of the angle A

• A. lies between 10${}^{\circ }$ and 20${}^{\circ }$
• B. lies between 20${}^{\circ }$ and 30${}^{\circ }$
• C. lies between 30${}^{\circ }$ and 40${}^{\circ }$
• D. lies between 40${}^{\circ }$ and 50${}^{\circ }$

Answer 1

The correct option is D

lies between 40${}^{\circ }$ and 50${}^{\circ }$

Let us construct the required triangle as follows:

Step 1:
Draw the base line AB of the length 2 cm.

Step 2:
Use your compass to make a circle with centre at point A and the radius 1 cm.

Step 3:
Use your compass to make a circle with centre at point B and the radius 1.5 cm.

Step 4:
In the point of intersection between the two circles, you'll find the point C.
Complete the triangle by drawing the lines between all three points, as shown below.

Now, by above construction, we see that the measure of $\angle$A is 46${}^{\circ }$.

Hence option (d) is the correct one.