Answer:
The triangle is a right triangle.
Step-by-step explanation:
Since The Pythagorean Theorem only works on right triangles, we can use this knowledge to prove whether this triangle is right:
![a^2 + b^2 = c^2\\10^2 + (2\sqrt{39})^2 = 16^2\\100 + (4 \times 39) = 256\\100 + 156 = 256\\256 = 256](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2%5C%5C10%5E2%20%2B%20%282%5Csqrt%7B39%7D%29%5E2%20%3D%2016%5E2%5C%5C100%20%2B%20%284%20%5Ctimes%2039%29%20%3D%20256%5C%5C100%20%2B%20156%20%3D%20256%5C%5C256%20%3D%20256)
Therefore, the triangle is right.
Given:
In triangle KLM, KL = 123 cm and measure of angle K is 35 degrees.
To find:
The length of the side KM to the nearest tenth of a centimeter.
Solution:
In a right angle triangle,
![\cos \theta =\dfrac{Base}{Hypotenuse}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%5Cdfrac%7BBase%7D%7BHypotenuse%7D)
In the given right triangle KLM,
![\cos K=\dfrac{KM}{KL}](https://tex.z-dn.net/?f=%5Ccos%20K%3D%5Cdfrac%7BKM%7D%7BKL%7D)
![\cos (35^\circ)=\dfrac{KM}{123}](https://tex.z-dn.net/?f=%5Ccos%20%2835%5E%5Ccirc%29%3D%5Cdfrac%7BKM%7D%7B123%7D)
![0.819152=\dfrac{KM}{123}](https://tex.z-dn.net/?f=0.819152%3D%5Cdfrac%7BKM%7D%7B123%7D)
Multiply both sides by 123.
![0.819152\times 123=KM](https://tex.z-dn.net/?f=0.819152%5Ctimes%20123%3DKM)
![100.755696=KM](https://tex.z-dn.net/?f=100.755696%3DKM)
![KM\approx 100.8](https://tex.z-dn.net/?f=KM%5Capprox%20100.8)
The measure of side KM is 100.8 cm.
Therefore, the correct option is (2).
Each person would receive 6 chocolate truffles and 4 caramel truffles because 126÷21=6 and 84÷21=4.
Answer:
Solution,
Radius(r)=6 cm
Height(h)=20 cm
Volume of cylinder= pi (r)^2 h
=3.14*(6)^2*20
=3.14*36*20
=2260.8 cm^3
Hope it helps
Good luck on your assignment
9514 1404 393
Answer:
x^2 -4x +2 = 0
Step-by-step explanation:
The other root is the conjugate of the given one, so is 2-√2. The quadratic equation in factored form is then ...
(x -2-√2)(x -2+√2) = 0
Expanding this, we get ...
(x -2)^2 -(√2)^2 = 0
x^2 -4x +4 -2 = 0
x^2 -4x +2 = 0 . . . . the equation you're looking for