Question

A water tower 30 m tall is located at the top of a hill. From a distance of D = 160 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.)

Answer 1

For this we need to use sinus law because there is no right angle in the observed triangle to solve it in some easier way.

$\frac{a}{sin( \alpha )} = \frac{b}{sin( \beta )}$

where a is height of the water tower, b is length from point of view till bottom of the tower, $\alpha$ is the angle from point of view and $\beta$ is angle opposite from b.

We use this law to calculate beta angle.

$sin( \beta ) = \frac{b}{a} *sin( \alpha )$

$sin( \beta ) = 0.742$
$\beta = 47,924$

Now we observe different angle. Bottom of the hill-top of the tower-point of view. We calculate angle at point of view (notice how it is different than previous one).

180-90-47.924 = 42.076

At last, the hill inclination is:
42.076 - 8 = 34.076 = 34.1