Question

∠A and ∠B are complementary angles of right triangle ABC, cos A = 0.83, and cos B = 0.55. What is sin A + sin B? 0.28 1 0.38 1.38

Answer 1

as you have given that angle A and B are complementary angles of right triangle ABC

so cos A=B/H=0.83
=83/100
this means that B=83 and H=100

now,using pythagoras theorem

H^2=B^2+p^2
100^2=83^2+p^2
10000=6889+p^2
10000-6889=p^2
3111=p^2
$\sqrt{?} 3111$
55.7763390695=P
we will take an approx. value for p
which is 55
now we have B=83 H=100 P=55

now sin A=p/h=BC/AB=83/100=0.83

SIMILARLY SIN B=P/H=AC/AB=55/100=0.55

NOW A.T.Q
SIN A + SIN B=0.83+0.55=1.38

SO LAST OPTION IS THE CORRECT ONE

HOPE IT WILL BE HELPFULL FOR YOU AND OTHERS ALSO