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2 years ago

Find the exact value of sin A in simplest radical form.

Mathematics

1 answer:

Scorpion4ik [409]2 years ago

5 0

Using the law of sines, we have

$\dfrac{AB}{\sin(C)}=\dfrac{BC}{\sin(A)}$

And we know that

$AB=\sqrt{85},\quad BC=6,\quad A=90$

So, the equation becomes

$\sin(A)=\dfrac{BC\sin(C)}{AB}=\dfrac{6\sin(90)}{\sqrt{85}}=\dfrac{6}{\sqrt{85}}$

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2 years ago

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If 1/4 inch equals 50 miles, find the miles represented by 4 1/2 inches.

Lostsunrise [7]

Answer:

900 miles

Step-by-step explanation:

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2 years ago

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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

2 years ago

Nancy had 333 dollars to spend on 9 books. After buying them she had 18 dollars. How much did each book cost ?

MissTica

Answer:

35 dollars

Step-by-step explanation:333-18=315 dollars

315/9=35 dollars for each book

7 0

2 years ago

7.2 - 3 C equals 2 c - 2

dolphi86 [110]

Answer:

9.2/5= C

Step-by-step explanation:

7.2- 3C = 2C -2 First, add the 2 on the other side to isolate 2C on one side

+2 +2

9.2 - 3C = 2C Next, add 3C to the other side

+3C +3C

9.2 = 5C Finally divide both sides by 5 to find the value of C

9.2/5= 5C/5

9.2/5 = C by dividing by 5 the 5 cancels out and you're left with the C value

5 0

2 years ago

Find the exact value of sin A in simplest radical form.​

Find the exact value of sin A in simplest radical form.