Question

Find BC to the nearest whole number.
Please explain how you got your answer. Thank you!
(There is a diagram)

Answer 1

\[\{\text{AB}=\text{BC} \tan (65 {}^{\circ}), \text{AB}=(\text{BC}+15) \tan (20 {}^{\circ})\} \]Solve the following for BC:\[\text{BC} \tan (65 {}^{\circ})=(\text{BC}+15) \tan (20 {}^{\circ}) \]

Answer 2

@robtobey In order to simplify to I put it into my calculator like tan(20)x15 = 5.459?

Answer 3

\[\text{BC}=\frac{15 \text{Tan}[20 {}^{\circ}]}{\text{Cot}[25 {}^{\circ}]-\text{Tan}[20 {}^{\circ}]} \]Yes. To help you out evaluate the above with a calculator. Mathematica says BC = 3.06624 to 6 digits.
By the way, \[\text{Cot}[25 {}^{\circ}]=\text{Tan}[65{}^{\circ}] \]

Answer 4

Thank you so very much. So, BC = 3, that's what I got but I went about it in a very clumsy manner. Thank you

Answer 5

You are welcome.