Question

a mouse on the ground is looking up at an owl sitting in a tree. the mouse’s line of sight to the owl creates an angle of 23° with the ground. the mouse is 31 meters from the tree. how high above the ground is the owl? round your answer to the nearest whole number.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle where the adjacent side to the \(23^\circ\) angle is \(31\) meters (distance from mouse to tree), and the opposite side is \(x\) (height of owl), so we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\).
\(\tan(23^\circ)=\frac{x}{31}\)

Step2: Solve for \(x\)

Multiply both sides by \(31\): \(x = 31\times\tan(23^\circ)\)
Calculate \(\tan(23^\circ)\approx0.4245\), then \(x = 31\times0.4245\approx13.1595\)

Step3: Round to nearest whole number

\(x\approx13\) (rounded to nearest whole number)

Answer:

13