Question 1176723
<br>
A student fairly early in his study of trigonometry should recognize the terms in this equation as those in the formula for tangent of the sum of two angles:<br>
{{{tan(A+B) = (tan(A)+tan(B))/(1-tan(A)*tan(B))}}}<br>
Manipulate the given equation to put it in that form:<br>
{{{tan(A)+tan(B)+tan(A)*tan(B) = 1}}}
{{{tan(A)+tan(B) = 1-tan(A)*tan(B)}}}
{{{(tan(A)+tan(B))/(1-tan(A)*tan(B)) = 1}}}
{{{tan(A+B) = 1}}}<br>
Since the tangent of 45 degrees is 1, this tells us A+B=45.<br>
But that together with the given that A-B=41 allows us to solve that pair of equations to find the measure of angle A.<br>
I leave that last little bit for you....<br>