Question

What is the approximate horizontal distance from the observatory to the island?

Answer 1

Tangent formula

`\tan (angle)=\frac{\text{opposite side}}{\text{ adjacent side}}`

Considering the angle of 25° in the diagram, the opposite side is the height of the observatory (150 ft) and the adjacent side is the horizontal distance from the observatory to the island (let's call it x). Substituting this information into the above formula:

`\begin{gathered} \tan (25\degree)=(150)/(x) \\ \tan (25\degree)\cdot(x)/(\tan (25\degree))=(150)/(x)\cdot(x)/(\tan (25\degree)) \\ x=(150)/(\tan (25\degree)) \\ x\approx322\text{ ft} \end{gathered}`

The horizontal distance from the observatory to the island is approximately 322 ft