Question

in a triangle ABC angle b is equals to 90 degrees and a b is equals to 4 cm BC is equals to 3 cm and ac is equals to 5 cm find sin a
explain step by step​

Answer 1

Step-by-step explanation:

1. draw base AB=4cm

2. with A as center, with a scale of 5cm as radius draw an arc and with B as center, with a scale of 6cm as radius draw an arc.

3. let C be the point of intersection of the above 2 lines.

4. draw a ray AX making an acute angle with line AB on the opposite side if the vertex C. 

5. mark 3 points A1,A2,A3 such tha A1A2=A2A3=A3A1

6. join A3B and draw a parallel line B′A2

7. draw a line parallel to BC  to intersect AC at C′

Thus AB′C′ is a required triangle.

Justification;

By construction,

ABAB′=AA3AA2=32

also B′C′∥BC

∴∠AB′C′=∠ABC

In △AB′C′,△ABC

∠A=∠A

∠AB′C′=∠ABC

△AB′C′∼△ABC

⇒ABAB′=ACAC′=BCB′C′

∴