We know that
tan ∅=opposite side angle ∅/adjacent side angle ∅
adjacent side angle ∅=opposite side angle/tan ∅
in this problem
see the attached figure to better understand the problemangle ∅=80°
opposite side angle ∅=12 ft (AB)
adjacent side angle ∅=? (AC)
adjacent side angle ∅=12/tan 80°------> 2.12 ft
the answer is2.12 ft
the complete question is
Find two numbers whose difference is 46 and whose product is a minimum
Let
x------->larger number
y-------> smaller number
P-------> product of the two numbers
we know that
-----> equation 1
-----> equation 2
substitute equation 1 in equation 2
![P=x*[x-46]\\ P=x^{2} -46x](https://tex.z-dn.net/?f=%20P%3Dx%2A%5Bx-46%5D%5C%5C%20P%3Dx%5E%7B2%7D%20-46x%20)
using a graph tool
see the attached figure
Find the value of x for that the product P is a minimum
the vertex is the point 
that means, for 
the product is a minimum 
find the value of y
therefore
the answer is
the numbers are 
and 
9.8 divided by 10\3
multiply both sides by 3 to get rid of the 3
(9.8 x3=29.4)then divide by 10 to get 2.94
Answer: 2100$
Step-by-step explanation:
The angle in the dilated figure is the same as the original angle in each case, a fact that should be confirmed by the way the answer choices are shown.
∠A = ∠A'
... 4x -4 = 51 -x
... 5x = 55
... x = 11
∠A = 4·11 -4 = 40 . . . . . . doesn't match any offered choice
___
∠B = ∠B'
... 6x -1 = 4x +21
... 2x = 22
... x = 11
... ∠B = 6·11 -1
... ∠B = ∠B' = 65 . . . . . matches selection D)
_____
∠C = ∠C'
... 8x -13 = 6x +9
... 2x = 22
... x = 11
... ∠C = 6·11 +9 = 75
... ∠C = ∠C' = 75 . . . . . matches selection D)
