In triangle PQR, the side length p = 12\text{ cm}, side length q = 18\text{ cm}, and \sin … — JAMB UTME

In triangle $PQR$ , the side length $p = 12\text{ cm}$ , side length $q = 18\text{ cm}$ , and $\sin P = 0.4$ . What is the exact value of $\sin Q$ ?

Answer: 0.6

The value of

\sin Q

is 0.6.

Applying the Sine Rule

\frac{p}{\sin P} = \frac{q}{\sin Q}

with

p = 12\text{ cm}

q = 18\text{ cm}

, and

\sin P = 0.4

gives

\frac{12}{0.4} = \frac{18}{\sin Q}

. Evaluating

\frac{12}{0.4} = 30

leads to

30 = \frac{18}{\sin Q}

, which yields

\sin Q = \frac{18}{30} = 0.6

State the Sine Rule equation for the given triangle sides and angles.

\frac{p}{\sin P} = \frac{q}{\sin Q}

The Sine Rule relates the lengths of the sides of a triangle to the sines of its opposite angles.

Substitute the known numerical values into the Sine Rule equation.

\frac{12}{0.4} = \frac{18}{\sin Q}

Substituting

p = 12

q = 18

, and

\sin P = 0.4

sets up an equation with a single unknown.

Simplify the left side of the equation and solve for

\sin Q

\sin Q = \frac{18}{30} = 0.6

Dividing 12 by 0.4 yields 30, so rearranging gives

\sin Q = \frac{18}{30} = 0.6

Using the Sine Rule to calculate an unknown sine ratio

Question