Question

20. In the adjoining figure, AABC is a right-angled
triangle in which ZB = 90°, ZA = 30 and AC = 20 cm
Find (1) BC, (ii) AB.
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Answer 1

Step-by-step explanation:

Given,

Angle B = 90°

So, AC is the Hypotenuse.

From the question, Hypotenuse = AC = 20 cm.

Now, Given Angle A = 30°

Apply sine

sinA = sin30

sinA = 1/2

But, We know that, sinA = Opposite side to A / Hypotenuse.

Opposite side to A is BC.

Now,

sinA = BC / AC

1/2 = BC / 20

BC = 10cm .

In the same way,

Apply cosine

cosA = cos30

cosA = √3/2

We know that, Adjacent side of A = AB

Now, cosA = AB/AC

√3/2 = AB/AC

√3/2 ( 20 ) = AB

10√3 = AB

BC = 10cm, AB = 10√3 cm