First, we simplify the fraction (0.9)/(0.6) to 1.5. Then, we multiply 12 by 1.5 to get the final value of b.

1. Solve for $x$ : $4x - 6 = 18$ 2. Calculate the area of a rectangle with a length of 12 cm and a width of 4 cm. 3. If $\cos(x) = 0.5$ , what is the value of $x$ in degrees? (Assume $0^\circ \le x \le 90^\circ$ ) 4. Factorize the quadratic expression: $x^2 + 7x + 12$ 5. Find the length of the hypotenuse of a right-angled triangle with sides 5 cm and 12 cm. 6. Find the derivative of $f(x) = 2x^3 + 3x^2 - x$ . 7. A bag contains 4 red balls and 6 blue balls. What is the probability of drawing a red ball? 8. Solve the following system of linear equations: $3x + y = 19$ $x - y = 2$ 9. Calculate the integral of $(4x^3 - 2x) \, dx$ . 10. In a triangle ABC, if side $a = 12$ , $\sin(A) = 0.6$ , and $\sin(B) = 0.9$ , what is the length of side $b$ ?

Answer: The length of side $b$ is $18$ .

Step-by-step solution

Step 1: Recall the Sine Rule

The Sine Rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. We will use this rule to find the unknown side $b$ .

Step 2: Substitute known values into the Sine Rule

We are given the length of side $a = 12$ , $\sin(A) = 0.6$ , and $\sin(B) = 0.9$ . We substitute these values into the Sine Rule equation.

Step 3: Solve for side b

To find $b$ , we rearrange the equation by multiplying both sides by $0.9$ . This isolates $b$ on one side of the equation.

Step 4: Calculate the value of b

First, we simplify the fraction $\frac{0.9}{0.6}$ to $1.5$ . Then, we multiply $12$ by $1.5$ to get the final value of $b$ .

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