Answer :
To solve this question, we will use trigonometry, specifically the tangent function, which relates the angle of an elevation to the ratio of the opposite side (length of the shadow) to the adjacent side (height of person) in a right angle triangle. Let's denote the length of the shadow as \( L \) and the height of the person as \( H \). The angle with the ground is given as \( \theta = 24^\circ \).
The tangent of an angle \( \theta \) in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In our case,
\[
\tan(\theta) = \frac{L}{H}
\]
where
\( \theta = 24^\circ \) (angle of elevation),
\( H = 1.82 \) m (height of the person),
\( L \) is what we need to find (length of the shadow).
We want to solve for \( L \), so we rearrange the equation:
\[
L = H \cdot \tan(\theta)
\]
Since our calculators work in radians, we could convert the degrees to radians, but here, we will skip that step because we're providing an analytical solution. However, if you were to convert, remember that \( 180^\circ \) is equivalent to \( \pi \) radians in case you use the conversion factor later on.
Now we can plug in the values we know:
\[
\tan(24^\circ) = \frac{L}{1.82}
\]
To find \( L \), we multiply both sides of the equation by 1.82 m:
\[
L = 1.82 \cdot \tan(24^\circ)
\]
Using a scientific calculator, you can find the value of \( \tan(24^\circ) \) and then multiply by 1.82 to get:
\[
L \approx 1.82 \cdot 0.4452 \text{ (rounded value of }\tan(24^\circ) \text{)}
\]
\[
L \approx 0.8107
\]
The length of the shadow \( L \) is approximately 0.81 meters. Therefore, the correct answer to the question is:
A. 0.81 m
