To find the total altitude of the helicopter, we start by determining its height above the ground level. We know that Hashim is on top of a 100-foot tall building and is looking at a helicopter at a 25-degree angle of elevation, which is 215 feet horizontally away from him.
We can use trigonometry to find the height of the helicopter above Hashim's position. Specifically, we can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle:
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]
In our case:
- \(\theta = 25^\circ\)
- The opposite side is the height of the helicopter above Hashim's position, which we'll call \(h\).
- The adjacent side is the horizontal distance from Hashim to the point directly below the helicopter, which is 215 feet.
Thus, we can set up the equation:
\[ \tan(25^\circ) = \frac{h}{215} \]
Now, we can solve for \(h\):
\[ h = 215 \cdot \tan(25^\circ) \]
Using a calculator to find \(\tan(25^\circ)\):
\[ \tan(25^\circ) \approx 0.4663 \]
Substituting back, we get:
\[ h \approx 215 \cdot 0.4663 \approx 100.276 \]
This means the height of the helicopter above Hashim is approximately 100.276 feet.
Now, to find the total altitude of the helicopter above ground level, we need to add the height of the building:
\[ \text{Total altitude} = \text{Height of building} + h = 100 + 100.276 \approx 200.276 \text{ feet} \]
Rounding this to two decimal places, the total altitude of the helicopter is approximately
\[ \boxed{200.28} \text{ feet} \]
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