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°
⇒[tex]\theta= 70^{\circ}[/tex]
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:
[tex]\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
From the given diagram;
[tex]\theta = 70^{\circ}[/tex]
Opposite side = Height of the Flag pole = h
Adjacent side = Shadow of the flagpole = 15 ft
Substitute these we get;
[tex]\tan 70^{\circ} = \frac{h}{15}[/tex]
Multiply both sides by 15 we get;
[tex]15 \cdot \tan 70^{\circ} = h[/tex]
[tex]15 \cdot 2.75 = h[/tex]
Simplify:
[tex]41.2 ft = h[/tex]
or
h = 41.2 ft
Therefore, the height of the flagpole is, 41.2 ft
