(5/12 - 1/4) ÷ (1/3 + 1/16)​

8/9 = 0.421052632

Step-by-step explanation:

(5/12 - 1/4) / (1/3+1/16)

Least common multiple of 12 and 4 is 12. Convert 5/12 and 1/4 o fractions with denominator 12.

5/12 - 3/12 / 1/3+1/16

Since 5/12 and 3/12 have the same denominator, subtract them by subtracting their numerators.

5-3/12 / 1/3+1/16

Subtract 3 from 5 to get 2.

2/12 / 1/3+1/16

Reduce the fraction 2/12 to lowest terms by extracting and canceling out 2.

1/6 / 1/3 + 1/16

Least common multiple of 3 and 16 is 48. Convert 1/3 and 1/16 to fractions with denominator 48.

1/6 / 16/48 = 3/48

Since 16/48 and 3/48 have the same denominator, add them by adding their numerators.

1/6 / 16+3/48

Add 16 and 3 to get 19.

1/6 / 19/48

Divide 1/6 by 19/48 by multiplying 1/6 by the reciprocal of 19/48

1/6 x (48/19)

Multiply 1/6 times 48/19 by multiplying numerator times numerator and denominator times denominator.

1 x 48/6 x 19

Do the multiplications in the fraction 1 x 48/6 x 19

48/114

Reduce the fraction 48/114  to lowest terms by extracting and canceling out 6.

8/19

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,