Using Trigonometry, the approximate distance from the observatory to the island is evaluated to be 322 feet.
Given Information
It is given that,
The height of the observatory = 150 feet
The angle of depression from the top of the observatory = 25°
We can calculate the horizontal distance of the observatory from the island using Trigonometry
What is Trigonometry?
The area of mathematics known as Trigonometry is concerned with certain functions of angles and how to use them in computations. There are six popular Trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their respective names and acronyms.
Calculating the Horizontal Distance Using Trigonometry
As per the rules of the Trigonometry,
[tex]tan \alpha = \frac{Perpendicular/ Opposite Side}{Base}[/tex]
Here,
[tex]\alpha[/tex] = 25°
Perpendicular = 150 ft.
Base = Horizontal Distance
Thus, [tex]tan 25 =\frac{150}{Horizontal Distance}[/tex]
∴ x ≈ 322 ft.
Learn more about Trigonometry here:
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