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2 years ago

Law of cosines HELP MES

Mathematics

1 answer:

Lorico [155]2 years ago

7 0

Answer:

70.52 degrees

Step-by-step explanation:

To find the angles, we must first find the lengths of each side of the triangle. Adding up the respective radii, we can see that

XY = 5+4 = 9 CM

XZ = 6+5 = 11 CM

ZY = 4+6 = 10 CM

Now we can apply the cosine rule

$C\:=\:\sqrt{A^2+B^2-2ABcosx}$

We need to rearrange the rule to solve for x, our missing angle

$x\:=\:cos^{-1}\left(\frac{a^2+b^2-c^2}{2ab}\right)$

solving for our unknown angle:

$x\:=\:cos^{-1}\left(\frac{9^2+10^2-11^2}{2\cdot 9\cdot 10}\right)$

$x\:=\:70.52^{\circ }$

Therefore angle YXZ is 70.52 degrees

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In triangle XYZ right angled at Y. Find the length of the hypotenuse if the length of the other two sides is 1.6 cm and 6.3 cm.

const2013 [10]

Answer:

6.5 cm

Step-by-step explanation:

From Pythagoras theorem

C^2= a^2 + b^2

Where a, b are the sides of the triangle

C= hypotenus sides of the triangle

two sides are given as 1.6 cm and 6.3cm respectively.

C^2= 1.6^2 + 6.3^2

C^2= 2.56 + 39.69

C^2 = 42.25

C= √42.25

C=6.5 cm

Hence, the length of the hypotenuse is 6.5 cm

7 0

2 years ago

PLEASE HELP FOR A BRAINLIEST!!!! Create your own example and explain how to solve Quadratic Equation using Quadratic Formula. Wh

SVETLANKA909090 [29]

Step-by-step explanation:

1. Create your own example and explain how to solve Quadratic Equation using Quadratic Formula.

The quadratic formula is used to solve quadratic equations. It is shown as $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

A quadratic equation is generally shown in the form of $ax^{2} +bx + c = 0$

For example, if you saw the equation $7x^{2} + 3x + 20 = 0$

7 would be $a$ , 3 would be $b$ , and 20 would be $c$ .

To solve the equation above, you would fill in the quadratic formula as such, $x=\dfrac{-3\pm\sqrt{(3)^2-4(7)(20)}}{2(7)}$

Then you could solve for x.

2. What part in the Quadratic Formula is the discriminant?

The discriminant is the equation under the square root on the quadratic formula, $b^{2} - 4ac$

It is tells us whether there are two solutions, one solutions, or no solutions.

3. How do you know the number of solutions based on the value of the discriminant?

To know the number of solutions based off of the value of the discriminant, you need to plug in your values. Using the example quadratic equation, $7x^{2} + 3x + 20 = 0$

We will plug the values into the discriminant.

$3^{2} - 4(7)(20) = -551$

Now, if the discriminant is positive it has two real solutions. If the discriminant is zero the equation has no real-number solutions. And finally, if the discriminant is negative, the equation has one real solution. Because our discriminant is -551, the example equation has one real solution.

Hope this helps! (Please consider Brainliest)

8 0

2 years ago

Geometry. Very basic.

AveGali [126]

Answer:

A)10.25 cm ; B)5 square cm

Step-by-step explanation:

Formula:

p=(a+b+c) [p= perimeter ; a,b , and c are the side lengths.]

∴The perimeter of the triangle =(4+2.75+3.5) cm

=10.25 cm

Formula:

A = 1/2 . b .h [A=area ; b= base ; h= height]

∴The area of the triangle = (1/2 . 4 . 2.5) square cm [b=4 ; h=2.5]

=5 square cm

6 0

2 years ago

Solve for x. Express the answer in simplest form.1/7 = 3/4x - 1

shtirl [24]

1/7 = 3/4x-1
3/4x=1/7+1=8/7
x=8/7*4/3=32/21

4 0

3 years ago

A rectangle has a perimeter of 42 m and a width of 9 m. What is the length in meters.

Vlad [161]

Answer:

12 meters

Step-by-step explanation:

2x9=18 (get both widths)

42-18=24 (take away widths of 9m)

24/2=12 (divide by 2 to get one length)

5 0

2 years ago