In triangle ABC, angle c is a right angle. if cos A= 5/8, what is the value of cos B? A. 3/8
1 answer:
Answer:
C. sqrt 39/8
Step-by-step explanation:
To solve this, we need to first draw the triangle.
cos Ф = adjacent / hypotenuse
cos A = 5/8 = adjacent / hypotenuse
From the diagram, when dealing with angle A, AB= hypotenuse = 8 and AC=adjacent =5
But when we are dealing with angle B , then BC becomes the adjacent and AC will now be the opposite, but AB still remains the hypotenuse, which implies, if we are looking for the value of COS B , we need to find side BC, we can easily do that using the Pythagoras theorem;
adjacent² + opposite² = hypotenuse²
adjacent² = hypotenuse² - opposite²
BC² = AB² - AC²
=8² - 5²
= 64 - 25
= 39
BC =√39
adjacent = √39 hypotenuse =8
cos B = adjacent / hypotenuse
cos B = √39 / 8
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