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Sindrei [870]
3 years ago
13

From a boat on the lake, the angle of elevation to the top of a cliff is 26°35'. If the base of the cliff is 85 feet from the bo

at, how high is the cliff (to the nearest foot)?

Mathematics
2 answers:
Trava [24]3 years ago
5 0
Check the picture below

now, <span>26°35' is just 26bdegrees and 35 minutes

your calculator most likely will have a button [ </span><span>° ' " ]  to enter degrees and minutes and seconds

there are 60 minutes in 1 degree and 60 seconds in 1 minute

so.. you could also just convert the 35' to 35/60 degrees

so </span>\bf 26^o35'\implies 26+\frac{35}{60}\implies \cfrac{1595}{60}\iff \cfrac{319}{12}&#10;\\\\\\&#10;tan(26^o35')\iff tan\left[ \left( \cfrac{391}{12} \right)^o \right]

now, the angle is in degrees, thus, make sure your calculator is in Degree mode

jek_recluse [69]3 years ago
5 0

Answer:

x=42.5 feet

Step-by-step explanation:

It is given that From a boat on the lake, the angle of elevation to the top of a cliff is 26°35'. If the base of the cliff is 85 feet from the boat, thus using trigonometry, we have

\frac{AB}{AC}=tan26^{\circ}35'

Substituting the given values, we get

\frac{x}{85}=tan26.6^{\circ}

⇒x=85(tan26.6^{\circ})

⇒x=85(0.500)

⇒x=42.5 feet

Therefore, the height of the cliff is 42.5 feet.

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