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

check the picture below

now, 26°35' is just 26bdegrees and 35 minutes

your calculator most likely will have a button [ ° ' " ] 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 [tex]\bf 26^o35'\implies 26+\frac{35}{60}\implies \cfrac{1595}{60}\iff \cfrac{319}{12} \\\\\\ tan(26^o35')\iff tan\left[ \left( \cfrac{391}{12} \right)^o \right][/tex]

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

boffeemadrid boffeemadrid · Answer 2 · 2019-05-31T08:11:41+02:00

Answer:

[tex]x=42.5 feet[/tex]

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

[tex]\frac{AB}{AC}=tan26^{\circ}35'[/tex]

Substituting the given values, we get

[tex]\frac{x}{85}=tan26.6^{\circ}[/tex]

⇒[tex]x=85(tan26.6^{\circ})[/tex]

⇒[tex]x=85(0.500)[/tex]

⇒[tex]x=42.5 feet[/tex]

Therefore, the height of the cliff is 42.5 feet.