Consider the diagram shown where a tree that is 100 ft tall casts a shadow 120 ft long. find the angle of elevation of the sun. (to the nearest degree)

39.80 degrees

Step-by-step explanation:

Given that in the diagram a tree of 100 feet height casts a shadow of 120 ft long

If we consider the angle of elevation it would be the angle of the triangle which the tip of the shadow makes with horizontal along the line of tip and top of tree.

If A is the angle of elevation then in the right triangle we have

tan A = opposite/adjacent side = height of tree/length of shadow

=100/120

= 5/6

A = arc tan (5/6) = 39.80

B. 40 degrees

Step-by-step explanation:

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752