Question

In a rectangle the angle between a diagonal and a side is 30 degree and the length of this diagonal is 8cm. The area of the rectangle is

Answer 1

Answer:

16√3 cm^2

Step-by-step explanation:

The diagonal of your rectangle will be a line that goes from the top left corner of your rectangle to the bottom right corner.

This line is the hypotenuse of your RIGHT triangle.

The problem tells us that the hypotenuse forms a 30 degree angle with on of the sides.

We can pick either side, but I chose to pick the side that includes the left side of the rectangle.

Now, we have a 30-60-90 right triangle. The base of the triangle is opposite the 30 degree angle, so it will equal x.

The hypotenuse is 2x cm and the height is x√3 cm.

So, since we know the hypotenuse is 8cm, we know:

8=2x and x=4; x√3=4√3

The area of a rectangle is b*h, so we multiply 4√3*4 to give us 16√3 cm^2.

Hope that helps.......

Pls mark as brainliest!!!

Answer 2

Answer:

Here, angle-30°,

Lenght= 8cm.

Cos30°=opposite/hypotenuse

√3/2=breadth/8

B=4√3

Using phythagoras theorem,

b²+l²=hypotenuse²

8²-(4√3)²=l²

l=4cm.

Area=l×b

Area=4*4√3

Area=16√3 cm²

HOPE IT HELPS :D