Question

"Question42
In the adjoining figure, ΔABC is a right-angled at B and Angle A =30° . If BC = 6 cm, find (1) AB, (2) AC.
Chapter6,T-Ratios of particular angles Exercise -6 ,Page number 290"

Answer 1

Hey there!

Given,
Triangle ABC is right angled at B,
Do, 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. Also from the question, It is BC = 6cm

Now,

sinA = BC / AC

1/2 = 6 / AC

AC = 6 * 2 = 12 cm.

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/12

√3/2 ( 12) = AB

6√3 = AB

$\therefore$ 1 ) AB = 6√3 cm, 2) AC = 12cm.

Answer 2

Solution.

Here,

1) Sin θ = perpendicular / Hypotenus

=> sin 30°= 6/ AC

=> 1/2= 6/AC [sin 30°= 1/2]

=> AC= 12cm

------------------------------

2) Now,

cos θ = Base/ Hypotenus

=> cos 30°= AB/ 12

=> √3/2 = AB /12

=> AB = 6√3 cm

___________________

[sorry i have not pen at this time..
please see drawn figure]

hope it helps you