Aguy wire to the top of a tower makes an angle of 75 o with the level ground. at a point 40 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 20 o. what is the length of the guy wire?

Step-by-step explanation:

See the picture in attached sheet. It shows the height of tower as h, length of wire as l.

Two right angled triangles are formed

From the triangles we make out that h/x=sin 75=0.9659

Or h =0.9659l

Base distance = l cos 75 = 0.2588l

From big right triangle, we have

tan 20 =

Or h =(0.2588l+40) (0.3640)

Equating two heights

0.9659l=(0.2588l+40) (0.3640)

=0.0942l+14.56

0.8717l=14.56

l=16.703 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

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day