Respuesta :
Answer:
x = 1568*tan(11°50')
x = 328.5 feet
x = 329 feet
Step-by-step explanation:
The height of the cliff is 328 feet.
Conversion of minutes into degrees
There are sixty minutes in every degree, by definition. To convert a number of minutes to degrees, divide the number of minutes by sixty.
According to the question
From a boat on the lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the boat, how high is the cliff (to the nearest foot)
Note that 11°50' is just 11 degrees and 50 minutes
60 minutes = 1 degree,
thus 50 minutes = x degree
= [tex]\frac{50}{60}[/tex] degrees
= 0.83°
Hence: 11°50' = 11.83°.
We solve using Trigonometric function of tan
[tex]tan \theta[/tex] = [tex]\frac{Opposite}{Adjacent}[/tex]
[tex]\theta[/tex] = 11.83°
Adjacent = 1568 feet
Opposite = Height of the cliff = x
[tex]tan 11.38^{0} = \frac{x}{1568}[/tex]
Cross Multiply
x = [tex]tan 11.83\times 1568[/tex]
x = 328.429195 feet
Approximately x = 328 feet (nearest foot)
Hence, the height of the cliff is 328 feet.
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