Hi friends,

The below is a question from a paper. Sorry it's in Afrikaans but I will explain. They give us information on the diagram, as well as the equations of two of the lines. In 4.1 we have to prove that ED is parralel to AB...I did that. Then 4.2 they say if E is the midpoint of BC, calculate the coordinates of B...I did that too...Please help with the next question...Calculate the angle CBA..and if I may, could you please explain to me what they mean with the next question which is to calculate the size of triangle CBA...do they mean the area?..All help will be greatly appreciated..Thank you.

 Nov 18, 2023

Two possible methods.

1. Calculate the lengths of AB, BC, CA and use the cosine rule to calculate angle CBA, then use the formula

area = BA.BC.sin(CBA)/2 to calculate the area. That requires you to calculate the lengths of the three sides..

2. Let the angle that CB makes with the x-axis be alpha, the angle that AB makes with the x-axis beta, then angle CBA, call it gamma, will be beta - alpha. From that

\(\displaystyle \tan\gamma=\tan(\beta-\alpha)=\frac{\tan\beta-\tan\alpha}{1+\tan\beta.\tan\alpha}. \)

\(\tan\beta \text{ and }\tan\alpha\)

are the slopes of the lines AB and CB respectively.

The area of the triangle can be calculated as the area of the trapezium minus the areas of two triangles.

If you are really keen, do it both ways and see that the answers are the same.

 Nov 18, 2023

Thank you, I do appreciate...will tackle them...

juriemagic  Nov 18, 2023

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