Question

In the rectangle abcd ab=12cm and angleBAC=30°calculate the length of side BC and the diagonal AC​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

GIVEN:

AB=12 cm.

∠BAC=30°.

SOLUTION:

Let's draw the rectangle.

Here, since it is a rectangle, the opposite sides will be equal.

Thus AB=CD=12 cm.

Now, In ΔCAB, we know that AD is 12 cm AND ∠BAC is 30°.

We can use cos(θ) = Adjacent/hypotenuse

Here the hypotenuse is AC, the adjacent side is AB = 12 cm.

Thus, cos (30°) = AB/AC

cos (30°)=12/AC-----(2)

But cos (30°) = 1/2-----(1)

From (1) and (2),

1/2=12/AC

AC=12×2

AC=24 cm.

Now, In ΔCAB, ∠B is 90°. Thus, ΔCAB is right-angled triangle.

Then we can use Pythagoras theorem:

AB²+BC²=AC²

12²+BC²=24²

BC²=24²-12²

BC=√432 cm.

BC=12√3 cm [SIMPLIFIED]

HOPE THIS HELPS :D