Question

If the minute hand of a clock sweeps an arc from 4 to 6 , find the angle through which it has rotated and the type of triangle formed. [3 MARKS]

Answer 1

Visualisation: 1 Mark
Finding the angle: 1 Mark
Type of Triangle: 1 Mark

The minute hand covers an angle of 30${}^{\circ }$ in every five minutes. The angle covered in moving from 4 to 6 is 60${}^{\circ }$.
The length of the minute hand remains constant. So the two sides of the triangle will be equal.
So the angles will be same for the sides which are equal.

Now, the angle included between the sides whose length are equal is 60${}^{\circ }$.
So the other angles are (180-60)$÷$2 = 60${}^{\circ }$.
Hence all the angles of the triangle are 60${}^{\circ }$.
$\therefore$ The the triangle formed is an equilateral triangle.