A 30 foot ladder leans against a house. The angle between the base of the ladder and the ground is 83º. Find the distance from the base of the ladder to the house. (Show work!)

3.656 ft

Round as needed

Step-by-step explanation:

cos∅ = adj/hyp

cos 83 = adj/30

multiply both sides by 30

30 * cos83 = adj

30 * 0.121869343405147 = adj

3.6560803022 = adj

≈ 3.656 ft

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