Question

How do I solve this problem? To find the distance AB across a river, a distance BC=250 is laid off on one side of the river. It is found that B =119 degrees and C=27 degrees. Find AB

Answer 1

`\begin{gathered} \text{To find A} \\ A+119+27=180 \\ A=180-119-27 \\ A=34 \\ U\sin g\text{ sine theorem} \\ (AB)/(\sin(27))=(BC)/(\sin(34)) \\ \text{Solving AB} \\ AB=(BC\sin(27))/(\sin(34)) \\ BC=250 \\ AB=(250\sin(27))/(\sin(34)) \\ AB=202.966\approx203 \\ \text{The distance AB is 203} \\ \\ \text{Question 2} \\ To\text{ find the }height\text{ of the h}ill \\ height\text{ = OB} \\ \tan (10)=(OB)/(600) \\ \text{Solving OB} \\ OB=600\tan (10) \\ OB=105.796\text{ fe}et\approx106\text{ fe}et \\ \text{The height of the hill is 106 ft} \\ To\text{ find the height of the antenna} \\ \text{Antenna}=OT-OB \\ \tan (25)=(OT)/(600) \\ \text{Solving OT} \\ OT=600\tan (25) \\ OT=279.78\text{feet}\approx279.8feet \\ \text{Hence} \\ \text{Antenna}=279.8feet-106\text{ fe}et \\ \text{Antenna}=137.8\text{ fe}et \\ \text{The height of the antenna is 137.8fe}et \end{gathered}`