Question

ERROR ANALYSIS Describe and correct the error in finding the length of GH


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Answer 1

Explanation:

the arc lenght is usually described by the following formula:

`l = \alpha * r`

where l is the arc length, alpha the angle(in radians) and r is the radius.

so in this case, using this formula we get

`l = 75 * ( (\pi)/(180)) * 5cm`

we are multiplying 75 x (pi/180) cuz, the angle has to be in radians. then

`l = (365)/(180) \pi \: cm = 6.54 \: cm \: \: aprox`

more sensible than the last result, considering that the total length of the circle is

L=2(pi)r

in this case L= 31.4 cm aprox

Answer 2

The error is that the central angle was not divided by 360 degrees. The correct length of arc GH is 25π/12 cm.

In Mathematics and Geometry, the arc length formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

Where:

• r represents the radius of a circle.
• θ represents the central angle.

By substituting the given parameters into the arc length formula, we have the following;

Arc length = 2πr × θ/360

Arc length = 2π(5) × 75/360

Arc length = 10π × 5/24

Arc length = 25π/12 cm.