Answer:
Therefore,
The area of the sector is 15.09 unit².
Step-by-step explanation:
Given:
Circle with,
radius = r = 6 unit
central angle = θ = 48°
pi = 3.143
To Find:
Area of sector = ?
Solution:
If 'θ' is in degree the area of sector is given as
Substituting the values we get
rounded to nearest hundredth
Therefore,
The area of the sector is 15.09 unit².
Answer:
AB = 75
BC = 60
AC = 45
m∠A = 53°
m∠B = 37°
m∠C = 90°
Step-by-step explanation:
<u>Trigonometric ratios</u>
where:
Given:
Therefore:
To find the length of AB (the hypotenuse), use Pythagoras’ Theorem:
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ AC² + BC² = AB²
⇒ 45² + 60² = AB²
⇒ AB² = 5625
⇒ AB = √5625
⇒ AB = 75
To find m∠A:
m∠C = 90° (as it is a right angle)
The interior angles of a triangle sum to 180°
⇒ m∠A + m∠B + m∠C = 180°
⇒ 53° + m∠B + 90° = 180°
⇒ m∠B = 180° - 53° - 90°
⇒ m∠B = 37°
Answer:
P( top two horses are predicted incorrectly in incorrect order)
=
Step-by-step explanation:
In the horse race the outcome can be predicted in 5! = 120 ways.
Now suppose the top two horses were predicted incorrectly in incorrect order. Now, the top horse can be predicted incorrectly in 4 ways.
Suppose the top horse was predicted to be in k-th position where k = 2, 3 ,4,5
so the second horse can be predicted to be in place from 1 to (k - 1)
So, the top two horses can be predicted incorrectly in incorrect order
in = 10 ways
and for each prediction of the two the remaining horses may be predicted in 3! = 6 ways.
Hence ,
P( top two horses are predicted incorrectly in incorrect order)
=
=
