(b) The diagram shows a metal plate made by removing a...

(b) The diagram shows a metal plate made by removing a segment from a circle with centre 0 and radius 8 cm. The line AB is a chord of the circle and angle AOB =2.4 Find: i. the length of AB ii. the perimeter of the plate iii. the area of the plate

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Transcript

00:01 Okay, so i see that you need help with this question and it says the diagram shows a metal plate made by removing a segment from a circle with a center o and radius 8 centimeters.

00:11 The line ab is the chord of the circle and the angle aob equals 2 .4.

00:18 So it says it wants to know the length of ab.

00:21 So the first thing that you have to do is it's 2 .4 radians and that equals approximately 138 degrees.

00:36 And what you have to do is you have to take c squared equals 8 squared plus 8 squared minus 2 times 8 times 8 times cosine of 138.

00:56 And so then you would take 8 squared plus 8 squared which is 64 plus 64.

01:04 I'll simplify that now.

01:07 So 64 plus 64 minus 128 times cosine 138.

01:17 So i'm going to get 128 minus and then when i multiply all this i'm going to get a negative 95 .123.

01:29 So i'm going to use my integer rules of keep, change, change.

01:33 So i'm going to add these two together and i'm going to get c squared equals 223 .123 and c squared equals or then what i'm going to do is i'm going to find the square root of both.

01:50 So c equals approximately 15.

01:53 I'm just going to round to the nearest whole number.

01:56 So that means that ab is approximately, line ab is approximately 15 units or centimeters we'll say.

02:12 Then it wants the perimeter of the plate...

Question

(b) The diagram shows a metal plate made by removing a segment from a circle with centre 0 and radius 8 cm. The line AB is a chord of the circle and angle AOB =2.4 Find: i. the length of AB ii. the perimeter of the plate iii. the area of the plate

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