Question

Answer it please guys.......please​

Answer 1

Required Answer:-

Given:

• ABCD is a rectangle.
• AC = 10cm.
• ∠ACB = 30°

To find:

• The length of AB and BC.

Solution:

Given that,

AC = 10

∠ACB = 30°

We know that,

➡ sin(30°) = 1/2

Here,

➡ sin(∠ACB) = 1/2

As sin is the ratio of the height to the hypotenuse, Therefore,

➡ AB/AC = 1/2

➡ AB/10 = 1/2

➡ AB = 1/2 × 10

➡ AB = 5cm.

➡ Hence, the length of AB is 5cm.

Now, By Pythagoras Theorem, we have,

➡ AB² + BC² = AC²

➡ 5² + BC² = 10²

➡ BC² = 100 - 25

➡ BC = √75

➡ BC = 5√3

➡ Hence, the length of BC is 5√3cm.

Answer:

• Length of AB is 5cm and length of BC is 5√3cm.

Verification:

We need to verify our result.

Here,

➡ ∠ACB = 30°

As ABCD is a Rectangle, Therefore,

➡ ∠B = 90°

Therefore,

➡ ∠BAC = 180° - (30° + 90°) = 60°

Now, we know that,

➡ cos(60°) = √3/2

We will check if the value remains same.

Here,

cos(∠BAC)

= 5√3/10 [Base/Hypotenuse]

= √3/2

Hence, the value remains same. So, our answer is correct (Verified)

Answer 2

Solved on the basis of class 10 chapter 9