Question

Find on x on this triangle

Answer 1

Answer: correct answer is B.

Explanation:

in the small triangle

taking 60 as reference angle

b =
`10√(3)`

so

tan 60 = p/b

`√(3)` = p/(
`10√(3)`)

30 = p

so

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

so

in bigger triangle

b = 20
`√(3)`

so

tan 45 = p/b

1 = p/(20
`√(3)`)

p = 20
`√(3)`

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

so

h^2 = (20
`√(3)`)^2 +( 20
`√(3)`)^2

= 1200 + 1200

h^2 = 2400

h =
`√(2400)`

=20
`√(6)`

so x = 20
`√(6)`