Question

Two birds spot a cat trying to jump up to their cage Find the angle of depression of the cat.

Answer 1

Step 1

Draw the triangle for clarity

From the diagram above it is clear, the angle of depression is equal to the angle of elevation since both angles are alternate interior angles. Therefore, we can go ahead to find the angle of elevation which is equal to the angle of depression.

Step 2

Find the angle of depression using SohCahToa

To find this angle we will use the ratio Cah written as

`\begin{gathered} \cos x=\frac{adjacent}{\text{hypotenuse}} \\ \text{adjacent}=4ft \\ \text{hypotenuse}=5ft \end{gathered}`

`\begin{gathered} \cos x=(4)/(5) \\ x=\cos ^(-1)((4)/(5)) \\ x=36.86989765^(\circ)_{} \\ x\approx36.9^(\circ)\text{ to 1 decimal places} \end{gathered}`

Hence the angle of depression of the cat, x to 1 decimal place = 36.9°