Answer:

Explanation:
Here, we want to get the percentage of the gross pay is the take-home pay
Mathematically, we have to divide the take-home pay by the gross pay and multiply it by 100%
Her take-home pay is the difference between her gross pay and her deductions
We have this as:

We have this as:
This is the formula of finding the hypotenuse: a² + b² = c².
So the legs would be a and b.
4² + 4² = c²
c² = 16 + 16
c² = 32
c = √32 (Option C)

Recall the half-angle identity:

So in order to find

, we only need to know the value of

. But there are two possible values. To decide which to take, we use the given information: we know that

lies in quadrant III, which means

, so

, which places

in quadrant II. In this quadrant, the sine of angle is positive, and so


is an angle of a ray whose terminal point,

lies on the circle

. The

-coordinate is all we need to know in order to find that

. So,
Answer:
The smallest angle is 32 degrees
Step-by-step explanation:
The given parameters show that the triangle is a right angled triangle;
Let the two other angles be represented by x and y;
Since the angle between side 5 cm and side 8 cm is 90, we can represent any of this sides as the opposite and as the adjacent;
Scenario 1 (Calculating x)
Let opposite = 5 cm
Let adjacent = 8 cm
In trigonometry, The relationship between opposite and adjacent is Tangent;



Take arctan of both sides


(Approximated)
Scenario 2 (Calculating y)
Let opposite = 8 cm
Let adjacent = 5 cm
In trigonometry, The relationship between opposite and adjacent is Tangent;



Take arctan of both sides


(Approximated)
<em>By comparing the angles, the smallest angle is 32 degrees</em>