Question

Find both the degree and the radian measures of the obtuse or acute angle formed by the hands of a clock at 8:00, at 2:00, and at 3:30. PLEASE AND THANK YOU <3

Answer 1

Assume the clock is a circle. We know there are 360 degrees in a circle. We know that clock shows 12 hours equally spaced around the clock. We also know there are two pi radians in a circle. We know an obtuse angle is between 90 degrees and 180 degrees.

So to solve the 8 o'clock problem we are looking at the angle formed between 8 and 12 as shown in figure a. We see that this distance spans 4 hours. 12-8=4 hours.

So now we use a proportion to solve for the angle in degrees for 8 o'clock.

4 hours angle in degrees
------- = -------------
12 hours 360 degrees.

So cross multiply 4 * 360 = 1440 Now divide by 12 and we get 1440/12= 120 degrees.

We can also use a proportion to solve for the angle in radians.

4 hours angle in radians
------ = -------------
12 hours 2*pi*radians

Let pi = 3.14

So cross multiply 4*3.14*2= 25.12 radians Now divide by 12 and we get 2.09 radians.