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 ACB = 60°
Now considering right triangle ABC we have;
sin60° = ABAC32 = AB215AB = 215×32 = 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;
sin30° = ABAC12 = AB215AB = 2152 = 107.50
And similarly we can find the height of the balloon from the ground as done above.

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