Answer:
Answers are :
x = 7.5 , y = [tex]\frac{15\sqrt{3} }{4}[/tex] , z = [tex]\frac{15\sqrt{3} }{2}[/tex]
a = 9.375 and b = 5.625
Step-by-step explanation:
From the attached figure , consider right triangle ABC.
∠B = 60° , BC = 15 {∵ BC = a + b}
We need to find AC = z
Using sin function,
i.e sin(60°) = [tex]\frac{AC}{BC}[/tex]
or sin(60°) = [tex]\frac{AC}{15}[/tex]
or AC = 15×sin(60°)
or AC = [tex]\frac{15\sqrt{3} }{2}[/tex]
Also, AB = x = 15×cos(60°) = [tex]\frac{15}{2} = 7.5[/tex]
Next,
Consider right triangle ADC
AD = y, AC = z = [tex]\frac{15\sqrt{3} }{2}[/tex]
∠C = 30°
Using sin function to get y.
i.e sin(30°) = [tex]\frac{AD}{AC} = \frac{y}{z}[/tex]
or sin(30°) = \frac{y}{[tex]\frac{15\sqrt{3} }{2}[/tex]}[/tex]
or y = [tex]\frac{15\sqrt{3} }{2}[/tex]×sin(30°)
or y = [tex]\frac{15\sqrt{3} }{4}[/tex]
Also, DC = b = [tex]\frac{15\sqrt{3} }{2}[/tex]×cos(30°)
b = [tex]\frac{45}{8} = 5.625[/tex]
Therefore, a= 15 - b = 15 - 5.625 = 9.375
Hence we got,
x = 7.5 , y = [tex]\frac{15\sqrt{3} }{4}[/tex] , z = [tex]\frac{15\sqrt{3} }{2}[/tex]
a = 9.375 and b = 5.625
