Question

A water tower 30 m tall is located at the top of a hill. From a distance of D = 125 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 the nearest tenth degree.

Answer 1

The angle of inclination of the hill is approximately 13.4 degrees

Step-by-step explanation:

To find the angle of inclination of the hill, we can use the concept of trigonometry. Let's label the height of the water tower as 'h' and the distance down the hill as 'd'. We can use the tangent function to find the angle of inclination:

tan(angle) = h / d

Using the given values of h = 30 m and D = 125 m, we can substitute them into the equation:

tan(angle) = 30 / 125

Now we can solve for the angle by taking the inverse tangent of both sides:

angle = atan(30 / 125)

Using a calculator, we can find that the angle is approximately 13.4 degrees.

Answer 2

the angle of inclination of the hill is 46.56°

Step-by-step explanation:

Given the data in the question;

Just as illustrated in the diagram below

so to find the angle of inclination of the hill;

sinA/30 = sinB/125

since angle BAC is 8°

we substitute

sin8°/30 = sinB/125

sinB = ( sin8°/30 ) × 125

B = sin⁻¹ ( ( sin8°/30 ) × 125 )

B = sin⁻¹ ( 0.004639 × 125 )

B = 35.44°

so since the some of a the angles of a triangle is 180;

A + B + C = 180

8° + 35.44° + C = 180

C = 180 - ( 8° + 35.44° )

C = 136.56°

Hence, Angle of inclination x will be;

x = 136.56° - 90°

x = 46.56°

Therefore, the angle of inclination of the hill is 46.56°