Given a circle with a radius of 2, which is the length of an arc measuring 75 degrees?

1 answer:

3 0

$\bf \textit{arc's length}\\\\
s=\cfrac{r\theta\pi }{180}\qquad 
\begin{cases}
\theta=\textit{angle in degrees}\\
r=radius\\
---------\\
r=2\\
\theta=75
\end{cases}\implies s=\cfrac{2\cdot 75\cdot \pi }{180}$

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A 5 mile jogging path diagonal divides a rectangular park in half. The park is 4 miles long. Find the width of the park.

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Answer: The required width of the park is 3 miles.

Step-by-step explanation: Given that a 5 mile jogging path diagonal divides a rectangular park in half and the park is 4 miles long.

We are to find the width of the park.

As shown in the attached figure below, the diagonal BD divides the rectangle ABCD into two equal parts,

where length DA = 5 miles, BD = 4 miles and AB = width = ?

Since each angle of a rectangle is right-angle, so triangle ABD will be a right-angled triangle.

Using Pythagoras theorem in triangle ABD, we have

$BD^2=AB^2+DA^2\\\\\Rightarrow AB=\sqrt{BD^2-DA^2}\\\\\Rightarrow AB=\sqrt{5^2-4^2}\\\\\Rightarrow AB=\sqrt{25-16}\\\\\Rightarrow AB=\sqrt{9}\\\\\Rightarrow AB=3.$