A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is 12 degrees . To the nearest foot, how far is the fire from the base of the tower?

99

Step-by-step explanation:

The angle of depression looking from the tower is the same as the angle of elevation looking at the top of the tower from the spot of the fire.  So, tan (12 degrees) = 21 / distance between the tower and fire.  Thus, the distance = 21 / tan(12).  

tan (12) = 0.2126

Distance = 21 / 0.2126 = 98.78

The question asks about the distance from the base to the fire (to the nearest foot.)  Thus, it is 99 feet.  

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²