Question

Finding the length of arc and and sector area? Genuinely confused and will mark for brainliest.

Answer 1

Answer:

Arc length = $=\frac{5}{4} \pi \,km=1.25\ \pi\,\,km$

$Area=\frac{25}{8}\, \pi\,\,km^2= 3.125\, \pi\,\,km^2$

Step-by-step explanation:

For the length of an arc of circumference, you need to recall the formula:

$arc = R * \theta$

which is the product of the radius R times the angle, but only valid if the angle $\theta$ is given in radians (not degrees). So we need to change the 45 degree angle into radians. we can do so by remembering that $\pi$ radians is the same as 180°, and then the following proportion can be written to find what is the value (x) of 45° in radians:

$\frac{45^o}{180^o} = \frac{x}\pi} \\x=\frac{45^o}{180^o} \,\pi\\x=\frac{\pi}{4}$

Now we find the length of the arc using the formula given above:

$arc = R * \theta\\arc=5\,km\,\frac{\pi}{4} \\arc=\frac{5}{4} \pi \,km$

Now for the area of the sector, recall the formula:

$Area = \frac{1}{2} R^2\,\theta$

with the same condition for $\theta$ of being expressed in radians (and not degrees). So the formula becomes:

$Area = \frac{1}{2} R^2\,\theta\\Area= \frac{1}{2} (5\,km)^2\,\frac{\pi}{4} \\Area=\frac{25}{8}\, \pi\,\,km^2$

Answer 2

Answer:

5 &x = 14

Step-by-step explanation: