Question

"Question41
In the adjoining figure, Δ ABC is a right - angled triangle in which Angle B = 90°, Angle A = 30° and AC =20cm. Find (1) BC (2) AB.
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 289"

Answer 1

Hey there!

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

$\therefore$ BC = 10cm, AB = 10√3 cm

Answer 2

One angle = 90°
Second angle = 30°
Remaining angle =180-90-30=60°

Appyling [from angle A] Cos∅ = base/hypotenuse

Cos30° = BC/AC

√3/2 = BC/20

10√3 = BC

-------
From angle B,

Cos60° = AB/20

1/2 = AB/20

10 = AB

===========

AB = 10 cm
BC = 10√3 cm

I hope this will help you

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