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