Question

Find the value of cosine for angle A

Answer 1

I believe the answer is 8/√89. Hope this helps.

Answer 2

Answer:  The cosine of angle A is $\dfrac{8\sqrt{89}}{89}.$

Step-by-step explanation:  We are given to find the value of cosine for angle A from the figure.

From the figure, we see that

triangle ABC is a right-angled triangle with ∠C = 90° and hypotenuse AB.

Also, AB = 8 ft and BC = 5 ft.

Using Pythagoras theorem in right-angled triangle ABC, we have

$AB^2=AC^2+BC^2\\\\\Rightarrow AB^2=8^2+5^2\\\\\Rightarrow AB=\sqrt{64+25}\\\\\Rightarrow AB=\sqrt{89}.$

Therefore, we get

$\cos \angle A=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos \angle A=\dfrac{AC}{AB}\\\\\\\Rightarrow \cos\angle A=\dfrac{8}{\sqrt{89}}\\\\\\\Rightarrow \cos\angle A=\dfrac{8\sqrt{89}}{89}.$

Thus, the cosine of angle A is $\dfrac{8\sqrt{89}}{89}.$