Question

The diagram shows a 9cm x 7cm rectangle-based pyramid. All the diagonal sides - TA, TB, TC and TD - are length 12cm. M is the midpoint of the rectangular base.

Work out angle TAC, to 1 decimal place.

I just need help with the extra two marks, I have gained 3 marks but I don't know how to continue.

Answer 1

Check the picture below.

`\cos(TAC )=\cfrac{\stackrel{opposite}{(√(130))/(2)}}{\underset{hypotenuse}{12}}\implies \cos(TAC)=\cfrac{√(130)}{24} \\\\\\ TAC=\cos^(-1)\left( \cfrac{√(130)}{24} \right)\implies TAC\approx 61.6^o`