Question

From a boat on the lake, the angle of elevation to the top of a cliff is 26°1'. If the base of the cliff is 205 feet from the boat, how high is the cliff (to the nearest foot)?

Answer 1

26° 1' = 26.0166666667°

tan (26.0166666) = opposite (or height) / 205
opposite (or height) = 205 * tan (26.0166666)
height = 205 * 1.2193797869
height = 249.97285632 feet
= 250 feet (rounded)

Answer 2

These were my choices @wolf1728 :
A) 113 ft
B) 110 ft
C) 103 ft
D) 100 ft

Answer 3

Oh I just discovered my mistake.
I obtained the tangent value from an Excel / Open Office spreadsheet and I forgot that the default value is radians NOT degrees - ARRGGHH !!!!!!!!!!!!!! Yes, radians are a convenient, natural unit of measure when dealing with calculus and sciences. HOWEVER, when someone is dealing with common, ordinary reality, having radians as a default value is an incredibly STUPID thing.

So the new equation becomes
height = 205 * 0.4880927253
height = 100.0590086787
height = 100 feet or D

I find it unsettling that my carpenter's square is uselessly calibrated in degrees as opposed to the easier to use radians. I mean doesn't everyone like to check their do it yourself weekend construction projects by making sure each corner of a room measures exactly 1.5707963268 radians?

Oh and once again, the height of that cliff is 100 feet. I'm hoping I used the correct unit instead of the much more logical furlongs or cubits.

and don't forget 100 feet = 9.8779 x 10-22 Megaparsecs