Question

Find the value of cosine for angle A

Answer 1

Answer: The cosine of angle A is
`(8√(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=√(64+25)\\\\\Rightarrow AB=√(89).`

Therefore, we get

`\cos \angle A=(base)/(hypotenuse)\\\\\\\Rightarrow \cos \angle A=(AC)/(AB)\\\\\\\Rightarrow \cos\angle A=(8)/(√(89))\\\\\\\Rightarrow \cos\angle A=(8√(89))/(89).`

Thus, the cosine of angle A is
`(8√(89))/(89).`