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

Answer:

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°