Question

Cherie is jogging around a circular track. She

Answer 1

Answer:

Measure of minor angle JOG is $95.5^{\circ}$

Step-by-step explanation:

Consider a circular track of radius 120 yards. Assume that Cherie starts from point J and runs 200 yards up to point G.  

$\therefore m JG = 200 yards, JO=120 yards$.  

Now the measure of minor arc is same as measure of central angle. Therefore minor angle is the central angle $\angle JOG = \theta$.

To calculate the central angle, use the arc length formula as follows.  

$Arc\:Length\left(s\right) = r\:\theta$  

Where $\theta$ is measured in radian.

Substituting the value,

$200=120\:\theta$  

Dividing both side by 120,

$\dfrac{200}{120}=\theta$  

Reducing the fraction into lowest form by dividing numerator and denominator by 40.

$\therefore \dfrac{5}{3}=\theta$  

Therefore value of central angle is $\angle JOG = \theta=\left(\dfrac{5}{3}\right)^{c}$, since angle is in radian

Now convert radian into degree by using following formula,

$1^{c}=\left(\dfrac{180}{\pi}\right)^{\circ}$

So multiplying $\theta$ with $\left(\dfrac{180}{\pi}\right)^{\circ}$ to convert it into degree.

$\left(\dfrac{5}{3}\right)^{c}=\left(\dfrac{5}{3}\right) \times \left(\dfrac{180}{\pi}\right)^{\circ}$

Simplifying,

$\therefore \theta = 95.49^{circ}$

So to nearest tenth, $\angle JOG=95.5^{circ}$