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