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
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Answered by
5
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
Answered by
23
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
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