In the adjoining figure ABCD is a rectangle with breath BC is equal to 7 cm and angle CAB is equal to 30°. Find the length of AB of the rectangle and the length of diagonal AC if the Cab angle is 60° then what is the size of the side AB of the rectangle.
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Given : ABCD is a rectangle with breath BC is equal to 7 cm and angle CAB b is equal to 30°
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
∠CAB = 60°
Tan ∠CAB = BC/AB
=> Tan 60° = 7 / AB
=> √3 = 7 / AB
=> AB = 7/√3 cm
Sin ∠CAB = BC/AC
=> Sin 60° = 7 / AC
=> √3/2 = 7 / AC
=> AC = 14/√3 cm
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