Find the missing length indicated<br> I WILL GIVE BRAINLIEST TI CORRECT ANT

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartF

Vsevolod [243]

First of all, this problem is properly done with the Law of Cosines, which tells us

$a^2 = b^2 + c^2 - 2 b c \cos A$

giving us a quadratic equation for b we can solve. But let's do it with the Law of Sines as asked.

$\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}$

We have c,a,A so the Law of Sines gives us sin C

$\sin C = \dfrac{c \sin A}{a} = \dfrac{5.4 \sin 20^\circ}{3.3} = 0.5597$

There are two possible triangle angles with this sine, supplementary angles, one acute, one obtuse:

$C_a = \arcsin(.5597) = 34.033^\circ$

$C_o = 180^\circ - C_a = 145.967^\circ$

Both of these make a valid triangle with A=20°. They give respective B's:

$B_a = 180^\circ - A - C_a = 125.967^\circ$

$B_o = 180^\circ - A - C_o = 14.033^\circ$

So we get two possibilities for b:

$b = \dfrac{a \sin B}{\sin A}$

$b_a = \dfrac{3.3 \sin 125.967^\circ}{\sin 20^\circ} = 7.8$

$b_o = \dfrac{3.3 \sin 14.033^\circ}{\sin 20^\circ} = 2.3$

Answer: 2.3 units and 7.8 units

Let's check it with the Law of Cosines:

$a^2 = b^2 + c^2 - 2 b c \cos A$

$0 = b^2 - (2 c \cos A)b + (c^2-a^2)$

There's a shortcut for the quadratic formula when the middle term is 'even.'

$b = c \cos A \pm \sqrt{c^2 \cos^2 A - (c^2-a^2)}$

$b = c \cos A \pm \sqrt{c^2( \cos^2 A - 1) + a^2}$

$b = 5.4 \cos 20 \pm \sqrt{5.4^2(\cos^2 20 -1) + 3.3^2}$

$b = 2.33958 \textrm{ or } 7.80910 \quad\checkmark$

Looks good.

6 0

3 years ago

Read 2 more answers

A sports store sells bicycle baskes at $40.00 for two. Another sports store sells bicycle baskets for $110 for five. Which store

Dennis_Churaev [7]

The first store sells baskets at the better rate because 40.00 divided by 2 is 20.00 dollars for one but 110 dollars divided by 5 is 22 dollars so by going to the first store you are saving 2 dollars.

4 0

3 years ago

A population of 490 bacteria is introduced into a culture and grows in number according to the equation below, where t is measur

Lera25 [3.4K]

Answer:

Rate of growth of bacteria when t=2 is 3.09 bacteria/hour

Step-by-step explanation:

As equation is not given so considering the Equation of growth of bacteria as

$P=490(1+\frac{4t}{50+t^{2}})$

We have to find the rate at which population is growing. To do so differentiate above equation w.r.to 't'

$\frac{dP}{dt}=\frac{d}{dt}490(1+\frac{4t}{50+t^{2}})\\\\\frac{dP}{dt}=490(\frac{d}{dt}(1)+\frac{d}{dt}(\frac{4t}{50+t^{2}}))\\\\\frac{dP}{dt}=490(0+\frac{4(50+t^{2})-(4t)(2t)}{(50+t^{2})^{2}})\\\\\frac{dP}{dt}=490(\frac{200+4t^{2}-8t^{2}}{(50+t^{2})^{2}})\\\\\frac{dP}{dt}=490(\frac{4(50-t^{2})}{(50+t^{2})^{2}})\\\\at\,\,t=2hours\\\\\frac{dP}{dt}=490(\frac{4(50-(2)^{2})}{(50+(2)^{2})^{2}})\\\\\\\frac{dP}{dt}=490(\frac{4(50-4)}{(50+4)^{2}})\\\\=3.09$

Rate of growth of bacteria when t=2 is 3.09 bacteria/hour

8 0

3 years ago

Which phrase describes an unknown or changeable quantity?

Assoli18 [71]

Hello!

An unknown or changeable quantity is a variable. We can write these expressions below and see which one has a variable.

A. 15

B. 60(5)

C. 2p

D. $3.76

As you can see, we do not know how many pages are in the book. Therefore, our answer is C.

I hope this helps!

4 0

3 years ago

Read 2 more answers

The length of two parallel sides of a trapezium are 5cm and 7cm and the area is 120cm.sq find the distance between the parallel

Alla [95]

The height or the distance between the two parallel sides of the given trapezium is 20 cm.

A trapezium or trapezoid is a two-dimensional geometric shape that has 4 sides, with one pair of parallel sides.

The parallel sides of a trapezium are called bases while the distance between them is the altitude or height.

The formula for the area of a trapezoid is given by

A = (a + b)/2 x h

where a and b are the parallel bases and h is the height.

Using this formula, the height or the distance between the two parallel sides can be computed.

A = (a + b)/2 x h

120 cm^2 = (5 cm + 7 cm) / 2 x h

120 = (12 / 2) x h

120 = 6h

h = 120 / 6

h = 20 cm

For more examples on solving the area of a trapezium, visit brainly.com/question/16904048.

#SPJ4

5 0

2 years ago

Find the missing length indicated I WILL GIVE BRAINLIEST TI CORRECT ANT