Answer:
B) 43 feet
Step-by-step explanation:
Let AB represents the height of pole and C represents the point on the ground ( shown in the below diagram ),
We need to find : Measure of AB.
Since, angle of depression from the top of a flag pole to a point on the ground is 30°,
By the alternative interior angle theorem,
m∠ACB = 30°,
∵ m∠ABC = 90°,
By the trigonometric ratio,
[tex]\tan 30^{\circ}=\frac{AB}{BC}[/tex]
We have BC = 75 ft,
[tex]\tan 30^{\circ}=\frac{AB}{75}[/tex]
[tex]\frac{1}{\sqrt{3}} = \frac{AB}{75}[/tex]
[tex]\implies AB = \frac{75}{\sqrt{3}}= 43.3012\approx 43[/tex]
Hence, the pole would be 43 ft tall ( approx )
