A ladder is placed against a wall as shown below.
The ladder is on level ground at an angle of 70° to
the horizontal. If the ladder is 7.85 feet up the wall,
how long is the ladder?

A. 7.4 ft
B. 30.7 ft
C. 28.8 ft
D. 8.4 ft

D. 8.4 ft

Step-by-step explanation:

The illustration forms a right angle triangle. The ladder is placed against the wall and it forms an angle of 70° with the ground. The ladder is 7.85 ft up the top the wall . The triangle formed, the opposite side is 7.85 ft which is the top of the ladder laying on the wall to the base of the wall. The length of the ladder is the hypotenuse of the ladder.

using sine ratio

sin 70° = opposite/hypotenuse

sin 70° = 7.85/h

cross multiply

h sin 70° = 7.85

divide both sides by sin 70°

h = 7.85/sin 70°

h = 7.85/0.93969262078

h = 8.35379551399

h ≈ 8.4 ft

h =

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3