Answer to Question #165430 in Trigonometry for Melody

Question

From the top of a cliff, Tony Stark can see a boat on the ocean. The angle of depression is 41°. If Tony Stark uses his laser range finder and determines that the boat is 1.4 kilometers away, how high is the cliff?

Answer 1

Solution.

Let $h$ be the height of the cliff, then

$$\sin{41°}=\frac{h}{1.4},$$

from here

$h=1.4\sin(41°)\approx 1.4•0.656=\\=0.9184\text{ kilometers}= 918.4\text{ meters.} \newline$

Answer. $0.9184\text{ kilometers, or } 918.4\text{ meters.} \newline$