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.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

answer: 1 + 1 = 11

step-by-step explanation: