Question

√x^2+5 and (20+x) are complimentary angles. Find the feasible value of x?

Answer 1

If √x^2+5 means √ ( x² + 5 ) then:

√ ( x² + 5 ) + 20° + x = 90°

√ ( x² + 5 ) = 90° - 20° - x

√ ( x² + 5 ) = 70° - x

Written mathematically:

√ ( x² + 5 ) = 70 - x

Square both sides

x² + 5 = ( 70 - x )²

x² + 5 = 70² - 2 ∙ 70 ∙ x + x²

x² + 5 = 4900 - 140 x + x²

Subtract x² from both sides

5 = 4900 - 140 x

Subtract 4900 from both sides

5 - 4900 = - 140 x

- 4855 = - 140 x

- 140 x = - 4895 =

x = - 4895 / - 140 = 4895 / 140

x = 5 ∙ 979 / 5 ∙ 28

x = 979 / 28

x = 34.96428571428°