Answer:
A ) a = 8[tex]\sqrt{3}[/tex] , c = 8[tex]\sqrt{6}[/tex]
B ) a = 2[tex]\sqrt{2}[/tex] , b = 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given as :
A ) ABC is right triangle , right angle at c
So, ∠ C = 90°
And ∠ A = 45° , ∠ B = 45°
And BC = a , CA = b , AB = c
measure of side b = 8[tex]\sqrt{3}[/tex]
Now, from right angle triangle ABC
Tan ∠ C = [tex]\dfrac{\textrm Perpendicular}{\textrm Base}[/tex]
Or, Tan 45° = [tex]\dfrac{\textrm a}{\textrm b}[/tex]
or, 1 = [tex]\dfrac{\textrm a}{\textrm8[tex]\sqrt{3}[/tex] }[/tex]
∴ a = 8[tex]\sqrt{3}[/tex]
Now, c² = a² + b²
Or, c² = ( 8[tex]\sqrt{3}[/tex] )² + (8[tex]\sqrt{3}[/tex] )²
Or, c = 8[tex]\sqrt{6}[/tex]
Again
B ) c = 4
So, Sin ∠ A = [tex]\dfrac{\textrm Perpendicular}{\textrm Hypotenuse}[/tex]
or , Sin 45° = [tex]\dfrac{\textrm a}{\textrm 4}[/tex]
Or , a = 4 × Sin 45°
∴ a = 4 ×[tex]\frac{1}{\sqrt{2} }[/tex]
I.e a = 2[tex]\sqrt{2}[/tex]
Now , b² = c² - a²
Or, b² = 4² - (2[tex]\sqrt{2}[/tex])²
Or, b² = 16 - 8 = 8
Or , b = 2[tex]\sqrt{2}[/tex]
Hence the solution of given expression
A ) a = 8[tex]\sqrt{3}[/tex] , c = 8[tex]\sqrt{6}[/tex]
B ) a = 2[tex]\sqrt{2}[/tex] , b = 2[tex]\sqrt{2}[/tex] Answer
