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3 years ago

Solve using trigonometry, find missing side

Mathematics

1 answer:

babymother [125]3 years ago

8 0

Answer:

Step-by-step explanation:

1. sin 30 = x/16

x= 16 sin 30

x = 8

2. cos 60 = 22/x

x = 22/cos 60

x = 44

3. tan 45 = x/19

x = 19 tan 45

x= 19

4. tan 16 = x/13

x = 13 tan 16

x= 3.73

5. sin 54 = x/45

x = 45 sin 54

x= 36.41

6. sin 35 = z/23

z = 23 sin 35

z = 13.19

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Find the exact value of sin2 theta given sin theta =5/13, 90°<theta <180°

Zepler [3.9K]

Now, we know that 90°< θ <180°, that simply means the angle θ is in the II quadrant, where sine is positive and cosine is negative.

$\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}$

$\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}
\\\\\\
therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}
\\\\
-------------------------------\\\\
sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13} \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}$

3 0

3 years ago

What is the length of CD ? In this diagram ABC EDC ?<br> Please help !!!!

n200080 [17]

Answer:
CD = x = 4 units

Explanation:
We are given that the two triangles are similar. This means that we can set the similarity proportionality as follows:
$\frac{BC}{CD} = \frac{CA}{CE} = \frac{AB}{ED}$

W e have:
BC = 20 - x
AC = 20
CD = x
CE = 5

Substitute in the above proportionality and solve for x as follows:
$\frac{20-x}{x} = \frac{20}{5} = 4$

4x = 20 - x
5x = 20
x = 4

Based on he above:
CD = 4 units
BC = 20 - x = 20 - 4 = 16 units

Hope this helps :)

5 0

3 years ago

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Determine if the pair of figures are congruent and select the appropriate theorem if applicable.

Korolek [52]

I think the answer should be A

5 0

2 years ago

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1. Alexis went shopping for school supplies with $80 in his bank account. He bought a bunch of binders for $23, pens and pencils

masha68 [24]

Answer: So alexis had $80 And he bought a bunch of binders for $23 So If you do the math you will get: $57 But then he buys pens and pencils for $16 So:

$57 - $16 = $41 And then he buys a new backpack for $37. So : $41 - $37 = $4

So yes he had enough to buy all the stuff and still had a little bit leftover!

Hope this helps!

Step-by-step explanation:

6 0

3 years ago

Car rentals involve a $130 flat fee and an additional cost of $31.67 a day what is the maximum number of days you can rent a car

Dmitry_Shevchenko [17]

The equation is $130 + $31.67x = 500
Subtract 130 from both sides $31.67x = $370
Divide $31.67 from both sides
X=11.68
BUT
you can’t have .68 of a day so the answer is 11 days.

8 0

3 years ago

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