SOLUTION: In a quadrilateral ABCD, AB=3cm, BC=5.7cm, CD=4cm and AD=4cm. AngleB=angle D=90 degree. Calculate the angle at A to 1 decimal place. This question is from the chapter trigonometr

Question 206805This question is from textbook Longman Mathematics for IGCSE Book1
: In a quadrilateral ABCD, AB=3cm, BC=5.7cm, CD=4cm and AD=4cm. AngleB=angle D=90 degree. Calculate the angle at A to 1 decimal place.
This question is from the chapter trigonometry:Tangent ratios.
I know that this question had already been solved,but the answer of this question is 101 as written at the back side of my course book.
It would certainly be a great pleasure for me if you solve my question again. Once again thankyou very very much! This question is from textbook Longman Mathematics for IGCSE Book1

Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
You know that two of the angles ar right angles.
Draw the quadrilateral using the lengths given AND making sure angels B and D are right angles.
Now, draw a line from A to C
Mark the angle CAB and call it alpha
Mark the angle CAD and call it beta
You now can use properties of tangents to find alpha and beat
alpha = inverse tan(BC/AB) = inverse tan (5.7/3) = 62.2
beta = inverse tan(CD/AD) = inverse tan(4/4) = 45
Now you know that alpha+beta = angle A
62.2+45 = 107.2
By my calculations, your book is wrong. it happens. Was the previous answer was also 107.2?
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