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Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

Find The Value Of Each Variable If Your Answer Is Not An Integer Express It In Simplest Radical Form class=

Sagot :

Answer:

a = 15

b = 5(6 - √3)

Step-by-step explanation:

Construction to be done in the given figure → Drop a perpendicular line (DE) from D to line AB.

From ΔAED,

cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

              = [tex]\frac{AE}{AD}[/tex]

cos(60°) = [tex]\frac{AE}{10\sqrt{3}}[/tex]

[tex]\frac{1}{2}=\frac{AE}{10\sqrt{3}}[/tex]

AE = [tex]5\sqrt{3}[/tex]

Since, b = AB - AE

b = (30 - 5√3)

b = 5(6 - √3)

By sine rule,

sin(60°) = [tex]\frac{\text{Oppositet side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{a}{10\sqrt{3}}[/tex]

a = [tex]\frac{30}{2}[/tex]

a = 15

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