I'll give you a brief explanation of the tangent ratio.
A right triangle has one right angle and 2 acute angles.
The right angle is opposite the longest side of the triangle. That side is called the hypotenuse.
The other two sides are the sides that form the right angle. They are called legs. The two legs may or may not have the same length, but the hypotenuse is always longer than either one of the legs.
The tangent ratio of trigonometry is the ratio of the lengths of the two legs.
It is a specific ratio using the legs in a specific order.
The tangent of an acute angle of a triangle is the ratio of the length of the opposite leg to the length of the adjacent leg.
I will use your triangle to explain the ratio.
Triangle XYZ has right angle Y.
The two acute angles are X and Z.
Triangle XYZ has a hypotenuse, side XZ, opposite the right angle.
Triangle XYZ has two legs, sides XY and YZ.
Since there is only one hypotenuse, if you mention the hypotenuse, you automatically know which side we are talking about. Since there are two legs, if I just mention "leg", you don't know which specific leg I mean. In order to know which specific leg I mean, I need to specify more. The legs are called adjacent leg and opposite leg. These terms are based on one of the acute angles.
The problem asks for the value of tan Z.
Z is one of the acute angles.
For angle Z, the adjacent leg is side YZ. Adjacent means "next to." The only leg next to angle Z is leg YZ.
For angle Z, XY is the opposite leg. Opposite means "across from." Leg XY is opposite angle Z.
Here is something you must memorize about the tangent ratio.
tan Z = (opp leg)/(adj leg)
The tangent is the ratio of the length of the opposite leg to the length of the adjacent leg.
tan Z = opp/adj
tan Z = 35/12
Answer: First choice.
Answer:
a)
b)
c)
Step-by-step explanation:
Answer:
82
Step-by-step explanation:
f(x) = 5x - 3
g(x) = 2x + 9
f(g(x)) = 5 (2x + 9) - 3 ..... replace x with g(x)
f(g(4)) = 5 * (2 * 4 + 9) -3 = 85 - 3 = 82
"97.5" will be the American women's % having their shoe sizes that are no more than 11.33.
Given values are:
- Mean = 8.33
- Standard deviation = 1.5
Now,
=
= (2 above Standard deviation)
→ The data values are between 8.33 and 11.33,
=
= (%)
→ The data value below 11.33,
= (%)
hence,
→ The percentage of American women will be:
=
= (%)
Thus the above answer is appropriate.
Learn more about empirical rule here:
brainly.com/question/18529739
Basis step: Let . Then
and
so .
Inductive step: Assume . We want to show that .
Now
where the first inequality follows from the induction hypothesis; the second follows from multiplying the right side by some ; and the third from adding the remaining terms to complete the binomial expansion , all of which are positive since they are some power of .
QED