Steps:
So before we can find line BC, we have to find Line BD. To do this, we will be using the pythagorean theorem, which is leg² + leg² = hypotenuse² . In this case, Line BA, which has a value of 16, is our hypotenuse and Lines AD, which has a value of 12, and BD, which has a value of x, are our legs. Set up our equation as such:
[tex]12^2+x^2=16^2[/tex]
Firstly, solve the exponents:
[tex]144+x^2=256[/tex]
Next, subtract both sides by 144:
[tex]x^2=112[/tex]
Next, square root both sides and line BD is √112 units (To get more accurate results, always leave approximation til the end of the problem.)
Now that we have line BD, we are going to be using trig ratios to solve for C. For Trig Ratios, remember "SOH CAH TOA" (θ = an angle)
- Sin(θ) = Opposite/Hypotenuse
- Cos(θ) = Adjacent/Hypotenuse
- Tan(θ) = Opposite/Adjacent
Since line BD does not touch the 40° angle, this makes BD the opposite side. And since line BC touches both the 40° angle and the right angle, this makes line BC the adjacent side. Since we have the opposite side and are solving for the adjacent side, we will be using Tan (or Tangent) to solve for the angle. Set up our equation as such (let y = BC):
[tex]\frac{\tan (40)}{1}=\frac{\sqrt{112}}{y}[/tex]
Firstly, cross multiply:
[tex]\sqrt{112}=\tan (40)*y[/tex]
Next, divide both sides by tan(40):
[tex]12.6=y[/tex]
Answer:
Line BC is 12.6 cm.
