An owl is 7 metres above ground level, in a tree - HSC - SSCE Mathematics Standard - Question 12 - 2019 - Paper 1

To find the horizontal distance to the mouse, we can use the formula relating the angle of depression, the height (opposite side), and the horizontal distance (adjacent side).

Using trigonometry, we know that: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Here, ( \theta = 32° ) and the height of the owl (opposite side) is 7 m. Therefore, we have:

$\tan(32°) = \frac{7}{d}$

Where ( d ) is the horizontal distance to the mouse. Rearranging gives us:

$d = \frac{7}{\tan(32°)}$

Calculating this value yields approximately:

$d \approx 7 / 0.62487 \approx 11.2 m$