Answer:
the distance from point C to D is 7.75m
Step-by-step explanation:
I think your question missed key information, allow me to add in and hope it will fit the orginal one. Please have a look at the attached photo
A vertical flagpole, AB,has a height of 46m. The points B, C and D lie on level ground, and BCD is a straight line Point C is 21 m from the base of the flagpole. The angle of elevation of the top of the flagpole from point D is 58 degrees
How far apart are points C and D?
My answer:
Given the infomation:
- AB: 46m
- BCD is a straight line
- BC = 21m
In triangle ABD, with angle of elevation from D to top of flag pole is 58 degrees.
<=> [tex]\tan \theta =\frac{perpendicular}{base}[/tex]
<=> tan(58) = [tex]\frac{AB}{BD}[/tex]
<=> BD = [tex]\frac{AB}{tan(58)}[/tex]
<=> BD = [tex]\frac{46}{1.6}[/tex]
<=> BD = 28.75
From the figure:
BD = BC + CD
<=> CD = BD - BC
<=> CD = 28.75 - 21 = 7.75m
So the distance from point C to D is 7.75m
