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.

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°

answer: ?

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .