The grad is a unit of angle measurement One grad is the meas

The \'grad\' is a unit of angle measurement. One grad is the measure of an angle that cuts off an are that is (1/400).if a circle\'s circumference. An angle that rotates a circle\'s circumference is 400 grads. Recall: If a circle has a radius of length r, then one con compute the length of the circle\'s circumference as 2 pi r. Suppose a protractor has a radius of 3.4 inches. Determine the length (in inches) of the are subtended by an angle measuring 90 grads. Show your work. An angle of 125 grads subtends what percent of a circle\'s circumference? Explain your answer.

Solution

a. 1 grad is the measure of the arc that is 1/400th of the circumference

And circumference=2pi*r=2*3.14*3.4=21.552

In 1 grad,length of arc=21.552/400

Therefore in 90 grad,length of arc=90*21.552/400=4.8042 inches

b. 1 grad is the measure of the arc that is equal to 1/400 th of the circumference

Therefore 125 grad is the measure of the arc that is equal to 125/400 of the circumference that is 5/16 of the circumference