Question

What is the value of cos A

Answer 1

The give diagram represents a right angled triangle with side AB and BC as follows,

`\begin{gathered} AB=24 \\ BC=7 \end{gathered}`

Apply the Pythagoras Theorem and solve for the hypotenuse,

`\begin{gathered} AC^2=AB^2+BC^2 \\ AC^2=(24)^2+(7)^2 \\ AC^2=576+49 \\ AC^2=625 \\ AC=\sqrt[]{625} \\ AC=25 \end{gathered}`

Now, apply the cosine ratio for angle A as follows,

`\begin{gathered} \cos A=(AB)/(AC) \\ \cos A=(24)/(25) \end{gathered}`

Thus, the cosine of angle A is equal to 24/25 .