#1**+3 **

Find AI using Pythagoras:

AI^{2} = (AC/2)^{2} + (18+5)^{2}

where AC^{2} = 5^{2} + 7^{2}

To find angle AIE first find length EI.

EI^{2} = (EH/2)^{2} + 5^{2} and EH = AC

Having found AI and EI, now use the cosine rule to find AIE:

cos(AIE) = (AI^{2} + EI^{2} - 18^{2})/(2*AI*EI) so AIE = cos^{-1}((AI^{2} + EI^{2 }- 18^{2})/(2*AI*EI))

I’ll leave you to crunch the numbers!

Alan
Mar 21, 2018

#1**+3 **

Best Answer

Find AI using Pythagoras:

AI^{2} = (AC/2)^{2} + (18+5)^{2}

where AC^{2} = 5^{2} + 7^{2}

To find angle AIE first find length EI.

EI^{2} = (EH/2)^{2} + 5^{2} and EH = AC

Having found AI and EI, now use the cosine rule to find AIE:

cos(AIE) = (AI^{2} + EI^{2} - 18^{2})/(2*AI*EI) so AIE = cos^{-1}((AI^{2} + EI^{2 }- 18^{2})/(2*AI*EI))

I’ll leave you to crunch the numbers!

Alan
Mar 21, 2018