Answer:
Option A is correct
the height of the flagpole is, 41.2 ft
Step-by-step explanation:
As per the statement:
The angle looking up at the sun is 70°
⇒![\theta= 70^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D%2070%5E%7B%5Ccirc%7D)
It is also given that:
A flagpole casts a shadow of 15 ft.
For this you can see the diagram as shown below in the attachment.
Now, find the height of the flagpole.
Let h be the height of flagpole.
using tangent ratio:
![\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B%5Ctext%7BOpposite%20side%7D%7D%7B%5Ctext%7BAdjacent%20side%7D%7D)
From the given diagram;
![\theta = 70^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2070%5E%7B%5Ccirc%7D)
Opposite side = Height of the Flag pole = h
Adjacent side = Shadow of the flagpole = 15 ft
Substitute these we get;
![\tan 70^{\circ} = \frac{h}{15}](https://tex.z-dn.net/?f=%5Ctan%2070%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7Bh%7D%7B15%7D)
Multiply both sides by 15 we get;
![15 \cdot \tan 70^{\circ} = h](https://tex.z-dn.net/?f=15%20%5Ccdot%20%5Ctan%2070%5E%7B%5Ccirc%7D%20%3D%20h)
![15 \cdot 2.75 = h](https://tex.z-dn.net/?f=15%20%5Ccdot%202.75%20%3D%20h)
Simplify:
![41.2 ft = h](https://tex.z-dn.net/?f=41.2%20ft%20%3D%20h)
or
h = 41.2 ft
Therefore, the height of the flagpole is, 41.2 ft