Séan makes a clinometer using a protractor, a straw, a piece of thread and a piece of plasticine (used as a weight) - Junior Cycle Mathematics - Question 13 - 2012

Using the tangent function:

$\tan(65°) = \frac{h}{10}$

We know that:

$h = 10 \times \tan(65°)$

Calculating: $h = 10 \times 2.1445$ gives $h = 21.445 \text{ m}$

Rounding to two decimal places, we get

h = 21.45 m.

The total height of the tree is calculated by adding Séan's height to the height calculated:

$\text{Total height} = h + ext{Séan's height} = 21.45 + 1.75$

Thus, the total height of the tree is

23.20 m.

One possible reason for the difference in height could be that the other student measured the angle of elevation differently, perhaps reading 64° instead of 65°. Small variations in angle can lead to significant differences in height calculations due to the tangent function’s sensitivity.