Answer:
55.53 feet.
Step-by-step explanation:
We have been given that a flagpole stands in the middle of a flat, level field. 50 feet away from its base, a surveyor measures the angle to the top of the flagpole as 48 degrees.
We can see from attached photo that flagpole, the surveyor forms a right triangle with respect to ground.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(48^{\circ})=\frac{h}{50}[/tex]
[tex]\text{tan}(48^{\circ})*50=\frac{h}{50}*50[/tex]
[tex]1.110612514829*50=h[/tex]
[tex]h=1.110612514829*50[/tex]
[tex]h=55.53062574[/tex]
[tex]h\approx 55.53[/tex]
Therefore, the height of the flagpole is approximately 55.53 feet.
