From the observation deck of a skyscraper, Micaela measures a 45° angle of depression to a ship in the harbor below. If the observation deck is 870 feet high,
what is the horizontal distance from the base of the skyscraper out to the ship?
Round your answer to the nearest hundredth of a foot if necessary.

870

Step-by-step explanation:

The angle we are focusing on is 45 degrees and we are given vaules/variables for the opposite and adjecent of the triangle. This means we use tangent. The opposite of the triangle is 870 and the adjacent is the unknown (x). The equation then simplifies to

tan(45)=870/x

tan(45)x=870

870/tan(45)=x

if you plug this into the caluclator you get 870.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b