To solve this we use trigonometric functions that would relate the hypotenuse y and the given values. For this case we use cosine function which is expressed as:
cosine theta = adjacent side / hypotenuse
cosine 52 = 35 / y
y = 35 / cos 52
y = 56.85
Rotation is a type of transformation refered to a in which the shape of the original object is preserved and the angle of rotation is constanf for all the parts of the body.
Thus, when <span>ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F.
</span><span>m∠EAE ' = m∠FAF '</span>
<span>if we take the centre of the circle as being the origin, we can say that
x coordinate is :cos o = x/r so x
= r cos o
</span><span>
and
y coordinate : cos(90-teta)= y/r
so y=r*cos(90-teta)
</span><span>
if teta is 29 degrees
y=r*cos(61)
and
x = r * cos(29)</span>
If the adjusted ratio was 2:7, then
2x is the number of pull-ups
and
7x is the number of box jumps.
You can state that since he completed 63 box jumps at the end of his training, then
7x=63,
x=9
and
2x=18.
The total number of exercises performed is 2x+9x=18+63=81.
As at start the ratio was 5:4, then
5y was the number of pull-ups
and
4y was the number of box jumps.
Therefore, 5y+4y=81,
9y=81,
y=9
and 5y=45, 4y=36.
Answer: Initially: 45 pull-ups and 36 box jumps. At the end: 18 pull-ups and 63 box jumps.
We first solve for angle TZU which is determined by the formula:
mTZU = 0.5(arcTU + arcSR)
mTZU = 0.5(72°+100°) = 86°
By vertical angle, mTZU = mSZR = 86°
We note that the sum of all angles formed is 360°. Solving for the remaining angles:
360° - 86° - 86° = 188°
Since mSZT is equal to mRZU by vertical angle, we divide 188° by 2.
188°/2 = 94°
m∠SZT = 94°
