Question

A trig question ask to proving an angle is 45 degrees?

In the quadrilateral ABCD sketched opposite, angle B and angle D are right angles, AB = 3BC = 3x and AD = 2DC = 2y. Use Pythagoras’ theorem and the cosine rule to show that angle A=45◦.

Answer 1

Please see below.

Explanation:

We have `tanA=tan(/_DAC+/_CAB)`

= `(tan/_DAC+tan/_CAB)/(1-tan/_DACtan/_CAB)`

= `(y/(2y)+x/(3x))/(1-y/(2y)*x/(3x))`

= `(1/2+1/3)/(1-1/2*1/3)`

= `(5/6)/(1-1/6)`

= `(5/6)/(5/6)`

= `1`

Hence `m/_A=45^@`