George Costanza is standing on top of a lighthouse that is 210 feet high. He sees his friends Jerry and Kramer in a boat. The angle of depression to the boat is 27°. If the lighthouse was built at sea level, find the distance from the boat to the foot of the lighthouse, to the nearest hundredth of a foot
Distance from boat to lighthouse -
feet

412.15 ft to the nearest hundredth

Step-by-step explanation:

You have to use the tangent function since you are given one leg of a right triangle and you are looking for the other leg

Let x = the distance from boat to lighthouse

So, tan 27 = 210/x

x tan 27 = 210

x = 210/tan 27

x = 412.14820  = 412.15 ft to the nearest hundredth

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.