Question

PLZZZZ HELP ASAP !!!!!

Answer 1

Explanation:

a.

`AC=√(AB^2-BC^2) =√(13^2-5^2) =√(169-25) =√(144) =12\\`

applying sine formula

AB=c

AC=b

BC=a

`(a)/(sin A) =(b)/(sin B) =(c)/(sin C) \\\\(5)/(sin A) =(12)/(sin B) =(13)/(sin 90) \\using~last~two\\(12)/(sin B)= (13)/(1) \\sin B=(12)/(13)\\ B=sin^(-1)((12)/(13)) \approx 67.38 ^\circ`

b.

third angle ∠Y=180-(30+90)=180-120=60

using sine formula

`(xz)/(sin Y) =(xy)/(sin Z) = (yz)/(sin X) \\(30)/(sin 60) =(xy)/(sin 90) =(h)/(sin 30) \\using ~first~and~last\\(30)/((√(3) )/(2) ) =(h)/((1)/(2) ) \\2h=(60)/(√(3) ) \\h=(30)/(√(3) ) * (√(3) )/(√(3) ) =10√(3)`