In \Delta ABC, \sin A = \frac{3}{5}, \sin B = \frac{4}{5}, and the side opposite angle A h… — JAMB UTME

In $\Delta ABC$ , $\sin A = \frac{3}{5}$ , $\sin B = \frac{4}{5}$ , and the side opposite angle $A$ has length $a = 15\text{ cm}$ . What is the length of side $b$ , in centimeters?

Answer: 20 cm

Answer

The length of side

b

is 20 cm.

Using the Sine Rule

\frac{a}{\sin A} = \frac{b}{\sin B}

, substitute

a = 15

\sin A = \frac{3}{5}

, and

\sin B = \frac{4}{5}

. Evaluating

\frac{15}{3/5}

gives

25

. Multiplying

25

\frac{4}{5}

yields

20\text{ cm}

Step-by-Step Solution

Set up the Sine Rule relationship between sides

a

b

and their opposite angles

A

B

\frac{a}{\sin A} = \frac{b}{\sin B}

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

Substitute

a = 15

\sin A = \frac{3}{5}

, and

\sin B = \frac{4}{5}

into the Sine Rule equation.

\frac{15}{3/5} = \frac{b}{4/5}

Direct substitution of known values allows us to solve for the unknown side

b

Simplify the left side of the equation.

15 \times \frac{5}{3} = 25

Dividing 15 by

\frac{3}{5}

is equivalent to multiplying 15 by

\frac{5}{3}

Multiply both sides by

\frac{4}{5}

to find

b

b = 25 \times \frac{4}{5} = 20\text{ cm}

Isolating

b

gives the final length of side

b

Key Concept

Sine Rule

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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