Answer:
1
Step-by-step explanation:
Using the trigonometric identities
tan(90 - x) = cotx , cotx = ![\frac{1}{tanx}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Btanx%7D)
Given
tan1tan2tan3....................... tan87tan88tan89
= tan1tan2tan3............... tan(90-3)tan(90-2)(tan90 - 1)
= tan1tan2tan3.............. cot3cot2cot1
= tan1cot1tan2cot2tan3cot3 ........................
= 1 × 1 × 1 ×....................... × 1
= 1
Answer:
red balls = 5
blue balls = 5
total balls = 5 blue+5 red
= 10
![p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls}](https://tex.z-dn.net/?f=p%28first%20%5C%3A%20ball%20%5C%3A%20being%20%5C%3A%20red%29%20%3D%20%20%5Cfrac%7Bred%20%5C%3A%20balls%7D%7Btotal%20%5C%3A%20balls%7D%20)
![p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2}](https://tex.z-dn.net/?f=p%28first%20%5C%3A%20ball%20%5C%3A%20being%20%5C%3A%20red%29%20%3D%20%20%5Cfrac%7B5%7D%7B10%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
Answer:
Arc Length = 68.7
Step-by-step explanation:
The formula that is used to find the arc length:
s = (θ/360) * 2πr
(You would get the value of θ, by subtracting 57 from 360)
(You would get r by dividing 26 by 2)
Now we can solve this;
s = (303/360) 2π(13)
s = 0.842 * 2π(13)
s = 0.842 * 0.283(13)
s = 68.7
Hope this helps!
Given:
LMN is an equilateral triangle.
LM = LN = MN = 12 cm
To find:
The height of the triangle h.
Solution:
In a right angle triangle,
![\sin \theta=\dfrac{Opposite}{Hypotenuse}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cdfrac%7BOpposite%7D%7BHypotenuse%7D)
![\sin (60^\circ)=\dfrac{h}{12}](https://tex.z-dn.net/?f=%5Csin%20%2860%5E%5Ccirc%29%3D%5Cdfrac%7Bh%7D%7B12%7D)
![\dfrac{\sqrt{3}}{2}=\dfrac{h}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D%5Cdfrac%7Bh%7D%7B12%7D)
Multiply both sides by 12.
![\dfrac{\sqrt{3}}{2}\times 12=\dfrac{h}{12}\times 12](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%5Ctimes%2012%3D%5Cdfrac%7Bh%7D%7B12%7D%5Ctimes%2012)
![6\sqrt{3}=h](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D%3Dh)
Therefore, the height of the triangle is
cm.