Question

An architect is sketching a doorway the top of which is part of a circle of radius 50 in the center angle is 100 how many inches long will the arc be?

Answer 1

Answer:

The arc length is 87.5 inches.

Step-by-step explanation:

Given that,

Arc length = S = ?

Angle = theta = 100°  

Radius = r = 50 inches

The relation between the arc length (S), angle (theta) and radius (r) is calculated using $S = r* \theta$

However, the angle should be in radian.

To convert degrees into radian, we use: $Degree * \frac{\pi}{180}$

=> $100 * \frac{\pi}{180}$

=> 1.75 radian

By putting values in the above relation, we get

$S = 1.75*50$

$S = 87.5 inches$

Therefore, the arc length is 87.5 inches.