The cosine for ∠A is [tex]\frac{5\sqrt{89} }{89}[/tex].
Option: A.
Step-by-step explanation:
From the given diagram,
Opposite = 8 ft.
Adjacent = 5 ft.
In trigonometry, the formula for cosine = [tex]\frac{adjacent}{hypotenuse}[/tex].
We are not given with hypotenuse. So we have to find the hypotenuse using Pythagorean Theorem [tex]hypotenuse = \sqrt{opposite^2+adjacent^2}[/tex]
[tex]hypotenuse = \sqrt{8^2+5^2}[/tex].
[tex]hypotenuse = \sqrt{64+25}[/tex].
hypotenuse = [tex]hypotenuse = \sqrt{89}[/tex].
cosine = [tex]\frac{5}{\sqrt{89} }[/tex].
Multiply [tex]\sqrt{89}[/tex] in both numerator and denominator,
The cosine for ∠A is [tex]\frac{5\sqrt{89} }{89}[/tex].
