Answers
I got answer 16.9
Step-by-step explanation:
1. Let's first look at triangle XYC. We know angle Y is 90 degrees because it has the symbol. and it is given that Angle X 45 degrees. Using the triangle interior angle theoreom, a triangle has 180 degrees so Angle C is 45 degrees. Know let find the sides, First we can deduce XY is 5 cm because of the triangle midsegment theorem XY is half of BC so since we know BC is 10 that means XY is 5. Then applying 45-45-90 triangle rules, XY=5, YC=5 and XC=[tex]5\sqrt{2}[/tex].
2.Now let look at the triangle XBC. Let find one missing angles. In the triangle . A angle bisector XC bisects XY and BC . Using that information Angle C of XYC = Angle C of XBC. So angle C=45 degrees. Knowing looking at the main triangle ABC Angle A=30, Angle C= 45+45=90 and Angle B=60 by interior triangle theorem. So going back to Angle X so angle x is 75 degrees due to interior triangle theorm. Also since Y=90 degrees it forms a linear pair to triangle AXY so Y=90 for AXY
Now let apply 30-60-90 triangle rules to AXY. XY =5, AY=[tex]5\sqrt{3}[/tex] and AX=10.
Finally. Apply 30-60-90 triangle rules to ABC. AC=[tex]5\sqrt{3}[/tex] +5 BC=10 and AB should turrn out to be 16.9.
This may not be right,but good luck:)
