Question 691245: In triangle ABC if angle A and angle B are acute angles and sin(a)=10/ 13 . What is the value of cos(A)?
can you please help me with this question? thanks in Advance
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! In a right triangle, sin(angle) = opposite side divided by the hypotenuse.
The cos(angle) = adjacent side divided by the hypotenuse. We need to use the Pythagorean Theorem from geometry to find the adjacent side and then it will be easy to see what cosine stands for.
a^2 + b^2 = c^2
(10)^2 + (adjacent side)^2 = (13)^2
100 + (adjacent side)^2 = 169
(adjacent side)^2 = 169 minus 100
(adjacent side)^2 = 69
After taking the square root of both sides of the equation, we find the adjacent side to be the square root of 69, which is written sqrt{69}.
Since cos(angle) is the adjacent side divided by the hypotenuse, cos(a) = sqrt{69}/13
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