Answer:
Let x equal the recurring decimal:
Create another number with recurring 216s by multiplying the above expression by 1000:
Subtract Equation 1 from Equation 2 to eliminate the recurring digits after the decimal:
Divide both sides by 999:
Simplify:
Answer: Tan B = 0.2917 (16.26 degrees)
Sin B = 0.2800 (16.26 degrees)
Cos B = 0.9600 (16.26 degrees)
Step-by-step explanation: Please refer to the picture attached for details.
The right angled triangle LNB has been drawn with the sides labeled as 7, 24 and 25 as indicated. With angle B as the reference angle, we can now identify each side as follows;
Side 7 (opposite, facing the reference angle)
Side 24 (adjacent, between the reference angle and the right angle)
Side 25 (hypotenuse, facing the right angle).
Hence, using the trigonometric ratios,
Tan B = opposite/adjacent
Tan B = 7/24
Tan B = 0.2917 (16.26 degrees)
Sin B = opposite/hypotenuse
Sin B = 7/25
Sin B = 0.2800 (16.26 degrees)
Cos B = adjacent/hypotenuse
Cos B = 24/25
Cos B = 0.9600 (16.26 degrees)
