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 trigonomet

Algebra ->  Trigonometry-basics -> 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 trigonomet      Log On


   

Question 206765This 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.
Please do help me solving this question. It is really difficult for me. Thankyou very much indeed! This question is from textbook Longman Mathematics For IGCSE book1

Answer by mickclns(59) About Me  (Show Source):
You can put this solution on YOUR website!

Since AD=CD and angle D is a right angle, Triangle ADC is an isosceles right triangle so angles DAC and DCA are 45 degrees.
 
The tangent of angle BAC (by SOH-CAH-TOA) is opposite%2Fadjacent+=+BC%2FBA+=+5.7%2F3+=+1.9
so the measure of angle BAC is arctan(1.9) = 62.2 On your calculator, arctan or inverse tangent is on the same button as tan, and looks like tan to the -1 power (which it isn't).
So the angle at A is the sum of the angles DAC and BAC which is 45 + 62.2 = 107.2 degrees.