a balloon is connected to an electric pole by a cable of length 215m inclined at 60 degree to the horizontal. determine the height of the balloon from the ground . also , find the height of the balloon if the angle of inclination is changed from 60 degree to 30 degree.

**Here it seems the data is missing. To find the height of the balloon , we should have the height of an electric pole which is not mentioned in the question.**

The figure below shows an electric pole CD and AE is the height of the balloon from the ground.

Here CD is the height of the electric pole.

And AC = 215 m and $\angle \mathrm{ACB}=60\xb0$

Now considering right triangle ABC we have;

$\mathrm{sin}60\xb0=\frac{\mathrm{AB}}{\mathrm{AC}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{\sqrt{3}}{2}=\frac{\mathrm{AB}}{215}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{AB}=215\times \frac{\sqrt{3}}{2}=186.19$

So to find the height of the balloon from the ground we have;

Height of the balloon = AB + BE = AB + CD = 186.19 m + CD; where CD is the height of electric pole

Similarly taking the angle as 30 degree, we have;

$\mathrm{sin}30\xb0=\frac{\mathrm{AB}}{\mathrm{AC}}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{1}{2}=\frac{\mathrm{AB}}{215}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{AB}=\frac{215}{2}=107.50$

And similarly we can find the height of the balloon from the ground as done above.

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