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Question

# The "grad" is a unit of angle measure that is sometimes used in France. One grad is the measure of an angle that cuts off an arc that is $\frac{1}{400} \mathrm{th}$ of a circle's circumference. An angle that rotates a circle's circumference is 400 grads. (Recall that one degree is an angle with vertex at the origin that cuts off an are that is $\frac{1}{360} \mathrm{th}$ of a circle's circumference and every circle's circumference is 360 degrees.) a. Using measures of circumference and arc length, explain how to make a protractor that measures an angle's openness in grads. b. If the protractor has a radius of 4.3 inches, determine the arc length in inches of: i. grad ii. 10 grads iii. 200 grads iv. 400 grads. c. An angle measuring 50 grads subtends what percent (or fractional part) of a circle's circumference? Explain your answer. d. How many degrees are equivalent to 50 grads? 100 grads? 10.2 grads? e. Define a function that converts a number of grads to a number of degrees. Explain how you determined this function.

Solution

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We are introduced wit the angle measure of the grad. We know that circles circumference in grad is:

$C=400~\text{grad}$

Where in degrees the circumference is::

$C=360°$

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