Bob tried to answer the following question by finding the missing angle and rounding the answer to the nearest degree.

here is his solution:
cos⁡x=16/20
x=cos^(-1)⁡(16/20)=36.8698976≈37°

bob made a mistake in his work. explain the mistake and write the correct solution.

1) Mistakes:

The adjacent side that is next to the missing angle is not 16, so is incorrect.

He should have used to find the missing angle.  

2) The correct solution is:

≈53°

Step-by-step explanation:

 Remember that:

1)  

If , then the angle whose cosine is A, can be calculated with the inverse function of the cosine:

2)

 If , then the angle whose sine is B, can be calculated with the inverse function of the sine:

The mistakes that Bob made, are:

The adjacent side of the right triangle is not 16, so is incorrect.

Knowing that the missing angle is "x", the opposite side and the hypotenuse are the known sides. Therefore, he should have used to find the missing angle.  

Therefore, the correct solution is:

≈53°

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

∞ this is your sign