Question

Find on x on this triangle

Answer 1

Answer: correct answer is B.

Step-by-step explanation:

in the small triangle

taking 60 as reference angle

b = $10\sqrt{3}$

so

tan 60 = p/b

$\sqrt{3}$ = p/($10\sqrt{3}$)

30 = p

so

$h^2 = p^2 + b^2\\ = 30^2 + (10\sqrt{3} )^2\\\\ = 900 + 300\\ = 1200\\so h^2 = 1200\\then, h = \sqrt{1200} \\ = 20\sqrt{3} \\so\\in bigger triangle\\\\h = x$(taking 45 as reference angle)

so

in bigger triangle

b = 20$\sqrt{3}$

so

tan 45 = p/b

1 = p/(20$\sqrt{3}$)

p = 20$\sqrt{3}$

so h^2 = p^2 + b^2

so

h^2 = (20$\sqrt{3}$)^2 +( 20$\sqrt{3}$)^2

= 1200 + 1200

h^2 = 2400

h =$\sqrt{2400}$

=20$\sqrt{6}$

so x = 20$\sqrt{6}$