Question

in a rectangle, the angle of between a diagonal and a side is 30and the length of the diagonal is 8 cm. find the area of the rectangle

Answer 1

Here,

given the length of diagonal = 8 cm

and angle between a side and diagonal = 30 °

so,

that side = 8 cos30

= 4√3 cm

and its perpendicular side = 8 sin30

= 8 × ½

= 4 cm

so,

area of Rectangle = 2 × area of two triangles formed

= 2 × ½ × 4 × 4√3

= 16√3 cm²

so,

Area of the rectangle = 16√3 cm²

Answer 2

Answer:

Let ABCD be the rectangle in which ∠BAC = 30o and AC = 8 cm.

In ∆BAC, we have:

ABAC= cos 30o = 3√2

⇒ AB8= 3√2

⇒ AB= 83√2= 43√ m

Again,

BCAC= sin 30o = 12

⇒ BC8= 12

⇒ BC =82= 4 m

∴ Area of the rectangle = (AB×BC) = (43√×4) = 163√ cm2