Astatue is mounted on top of a 21 foot hill. from the base of the hill to where you are standing is 57feet and the statue subtends an angle of 7.1° to where you are standing. find the height of the statue.

Please find the attached diagram for a better understanding of the question.

As we can see from the diagram,

RQ = 21 feet = height of the hill

PQ = 57 feet = Distance between you and the base of the hill

SR= h=height of the statue

=Angle subtended by the statue to where you are standing.

= which is unknown.

Let us begin solving now. The first step is to find the angle which can be found by using the following trigonometric ratio in :

Which gives to be:

Now, we know that and can be added to give us the complete angle in the right triangle .

We can again use the tan trigonometric ratio in to solve for the height of the statue, h.

This can be done as:

Thus, the height of the statue is approximately, 8.45 feet.

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step-by-step explanation: