As part of an examination a few years ago, a student went through the algebraic manipulations on an exam shown below. At this point you don't know what the symbols mean, but given the information at the left about the dimensions associated with each symbol, decide a. Is it possible that the final equation is correct? Show using dimensional analysis.
b. If the final equation is not correct, does that mean that the starting equation is necessarily wrong? Again, show using dimensional analysis.
c. If the final equation is not correct and the starting equation is not wrong, can you find the error using dimensional analysis?
[M] = M [g]=L/T2 [h]=L []=1/T [v]=L/T [R]=L [I]=ML2

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).