Question

In the following figure ABCD is a rectangle with breath BC is equal to 7 cm and angle c a b is equal to 30 degrees find the length of AB of the rectangle and the length of diagonal AC if the Cab angle is 30° then what is the size of the side AB of the rectangle

Answer 1

Given :  ABCD is a rectangle with breath BC is equal to 7 cm and angle c a b is equal to 30 degrees

To Find :   length of AB of the rectangle and the length of diagonal AC

Solution:

ABCD is rectangle

∠B = 90°

∠CAB = 30°

Tan ∠CAB =  BC/AB

=> Tan 30° = 7 / AB

=> 1/√3 = 7 / AB

=> AB = 7√3 cm

Sin ∠CAB =  BC/AC

=> Sin 30° = 7 / AC

=> 1/2 = 7 / AC

=> AC = 14  cm

AB = 7√3 cm  , AC = 14  cm  

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