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3 years ago

If sin 150° is 1/2 find sin75°

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

7 0

Answer:

use a calculator and enter those numbers then press SIN

Step-by-step explanation:

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Does anyone know how to do this ??? -view attachment

cricket20 [7]

As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.

The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.

To find angle-B, the law of cosines says

   b² = a² + c² - 2 a c cosine(B)

B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9

(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)

   1.96 = (1) + (3.61) - (3.8) cos(B)

Add 3.8 cos(B) from each side:

   1.96 + 3.8 cos(B) = 4.61

Subtract 1.96 from each side:

   3.8 cos(B) = 2.65

Divide each side by 3.8 :

cos(B) = 0.69737 (rounded)

Whipping out the
trusty calculator:
   B = the angle whose cosine is 0.69737

      = 45.784° .

Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...

By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !

8 0

3 years ago

Meeta buys a ticket for the movie and a popcorn, which costs $6. She spends $16.50 in all. How much was the movie ticket?

Sav [38]

Answer:

10.50

Step-by-step explanation:

16.50-6

6 0

2 years ago

The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

Can someone help me out please

ArbitrLikvidat [17]

B) AAS Congruence Theorem
(correct answer i promise)

explanation:
The Angle Angle Side postulate (often abbreviated as AAS) states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

6 0

3 years ago

Evaluate x(y+3)/(3+y)z for x=12, y=1, and z=6. A) 2 B) 5 C) 8 D) 6

fgiga [73]

Answer:

Step-by-step explanation:

We take the equation

$x(y+3)/(3+y)z$