Awater tower 30 m tall is located at the top of a hill. from a distance of d = 110 m down the hill it is observed that the angle formed between the top and base of the tower is 8°. find the angle of inclination of the hill. (round your answer to one decimal place.)

Step-by-step explanation:

Application of Right Triangles

The right triangles have an internal angle of 90°, we can take advantage of it because the fundamental trigonometric functions can be expressed to relate angles and lengths in a right triangle.  

Please refer to the image below to understand the upcoming relations and variables. The lower triangle has an angle \theta and h_h and D are the opposite and adjacent legs respectively, then:

Where h_h is the height of the tower. We can solve:

For the big triangle:

Where is 8° and is the height of the hill. Knowing that:

We replace it into the above equation

We have an equation in , but we need to expand the tangent of a sum of angles:

Rearranging

Multiplying

Simplifying, we have a second-degree equation for tan\theta

Using the known values D=110, ht=30,

Solving the equation, we get two answers:

This solution is not feasible, since the angle cannot exceed 90° or go below 0°, thus the other answer

is the correct option. Computing the angle of inclination of the hill:

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743