SOLUTION: In right triangle ABC, angle A and angle B are complementary angles. The value of cos A is 5/13. What is the value of sin B?

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Question 868502: In right triangle ABC, angle A and angle B are complementary angles. The value of cos A is 5/13. What is the value of sin B?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

Since A and B are complementary,
A%2BB=90
cos%28A%2BB%29=0
But you also know,
cos%28A%2BB%29=cos%28A%29cos%28B%29-sin%28A%29sin%28B%29
cos%28A%29cos%28B%29=sin%28A%29sin%28B%29
.
.
Since,
cos%5E2%28A%29%2Bsin%5E2%28A%29=1
25%2F169%2Bsin%5E2%28A%29=1
sin%5E2%28A%29=144%2F169
sin%28A%29=12%2F13
.
.
Substituting,

You also know that,
cos%5E2%28B%29%2Bsin%5E2%28B%29=1
%28144%2F25%29sin%5E2%28B%29%2Bsin%5E2%28B%29=1
%28169%2F25%29sin%5E2%28B%29=1
sin%5E2%28B%29=25%2F169
highlight%28sin%28B%29=5%2F13%29