A statue is mounted on top of a 16 foot hill. From the base of the hill to where you are standing is 77 feet and the statue subt
ends an angle of 13.2° to where you are standing. Find the height of the statue.
2 answers:
Imagine a right triangle where vertex B is at the base of the hill, vertex S is at the top of the statue, and vertex Y represents your position. This triangle has a right angle at B, and angle Y measures 13.2°. Let h denote the height of the statue, making the lengths of sides YB and BS equal to 77 ft and 16+h ft, respectively.
With the lengths of two sides and one angle known, the height h can be determined using the tangent function:
ft.
Result: the height of the statue calculates to be 2.0565 ft.
The statue's height is 19.8 feet
Detailed explanation
To begin with, let’s explore the principles of trigonometry in mathematics.
Consider triangle ΔABC as a right triangle with ∠A equal to 90°.
The relationships can be stated as: sin ∠A = opposite / hypotenuse, cos ∠A = adjacent / hypotenuse, and tan ∠A = opposite / adjacent
There are various trigonometric identities to recall, such as
Now, let's proceed with solving the problem!
Examine triangle ΔABC found in the provided figure.
We will employ this equation to determine ∠BAC:
tan ∠BAC = opposite / adjacent
Now consider triangle ΔABD from the figure.
We will use this equation to determine BD:
tan ∠BAD = opposite / adjacent
In conclusion, the statue's height corresponds with CD:
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Answer details
Grade: College
Subject: Mathematics
Chapter:TrigonometryKeywords:
Sine, Cosine, Tangent, Opposite, Adjacent, Hypotenuse, Triangle, Fraction, Lowest, Function, Angle
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