If a 20 foot ladder makes a 50 degree angle with the ground, how many feet up a wall will it reach. Round to the nearest tenth.

The ladder would reach 15.3 ft up the wall

Step-by-step explanation: Please refer to the attached diagram.

If the ladder (represented by line AC) rests on the wall (represented by line AB), it forms an angle of 50 with the ground (at point C). The ground is represented by line BC.

We need to remember that we have one side and one angle given in this question. The given side is the hypotenuse (the side facing the right angle, B in this case) and the given angle is the reference angle. The unknown side which is x, is the opposite as it is facing the reference angle.

Having the opposite and the hypotenuse, we can use the Sine ratio which is,

Sine C = opposite/hypotenuse

Sine 50 = x/20

Checking our table of values or by use of our calculator, sin 50 is 0.766

Sin 50 = x/20

0.766 = x/20

By cross multiplication, we now have our equation rewritten as;

0.766 (20) = x

15.32 = x

Rounded to the nearest tenth,

x = 15.3 ft

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: