Question

Which expression shows the height, in meters, of the sail?

Answer 1

Solution:

Let h represent the required height

To determne the value of h, we can use the trigonometric ratio (SOH-CAH-TOA)

Opposite = h

Adjacent = 2m

$\begin{gathered} tan40=\frac{h}{2} \\ \\ Take\text{ the inverse of both sides} \\ \frac{1}{tan40}=\frac{2}{h} \\ \\ But\text{ }\frac{1}{tan\theta}=cot\theta \\ \\ Thus,\text{ } \\ \frac{1}{tan\text{ 40 }}=cot40 \\ \\ Hence,\text{ }\frac{1}{tan40}=\frac{2}{h}\text{ becomes cot40 = }\frac{2}{h} \\ \\ cross\text{ multiply} \\ h\text{ x cot40 = 2} \\ h=\frac{2}{cot40} \end{gathered}$

The last option is the correct option.