Question

find length bc
4.7 cm
26°
a
b
c
a4 find

Explanation:

Step1: Identify triangle type

It's a right - triangle at B, with angle at A = 26°, hypotenuse AB = 4.7 cm, and we need to find BC (opposite to angle A).

Step2: Use trigonometric ratio

We know that in a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 26^{\circ}$, opposite side is BC, and hypotenuse AB = 4.7 cm. So, $\sin(26^{\circ})=\frac{BC}{4.7}$.

Step3: Solve for BC

Multiply both sides by 4.7: $BC = 4.7\times\sin(26^{\circ})$. Calculate $\sin(26^{\circ})\approx0.4384$. Then $BC\approx4.7\times0.4384\approx2.06$ cm.

Answer:

The length of BC is approximately 2.06 cm.