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3 years ago

How to find geometry of an unequal length triangle with angles known?

Mathematics

1 answer:

lana66690 [7]3 years ago

8 0

Use the cosine or sin rule, depending on the question.

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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

Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept fo

Alla [95]

Answer:

$\displaystyle y=-\frac{1}{2}x+4$

Step-by-step explanation:

<u>Equation of a Line</u>

We can find the equation of a line by using two sets of data. It can be a pair of ordered pairs, or the slope and a point, or the slope and the y-intercept, or many other combinations of appropriate data.

We are given a line

$y - 12 = 2x -8$

And are required to find a line perpendicular to that line. Let's find the slope of the given line. Solving for y

$y = 2x +4$

The coefficient of the x is the slope

$m=2$

The slope of the perpendicular line is the negative reciprocal of m, thus

$\displaystyle m'=-\frac{1}{2}$

We know the second line passes through (2,3). That is enough information to find the second equation:

$y-y_o=m'(x-x_o)$

$\displaystyle y-3=-\frac{1}{2}(x-2)$

Operating

$\displaystyle y=-\frac{1}{2}(x-2)+3$

Simplifying

$\displaystyle y=-\frac{1}{2}x+4$

That is the equation in slope-intercept form. Intercept: y=4

8 0

2 years ago

What is 75% of 180?

OverLord2011 [107]

Hello There!

75% of 180 is 135.

Converting Percent To Decimal.

p = 75%/100 = 0.75

Y = 0.75 * 180

Y = 135

3 0

2 years ago

Read 2 more answers

If 2000 is placed into a bank account that pays 3% compound interest per year how much will be in the account after 2 years

Margarita [4]

Answer:

Account Balance = Principal x (1 + interest rate (decimal)) number of years, compounded annually.

Step-by-step explanation:

This is based on the information provided: 2121.80 (1.03)2 = 2000 So, on your initial deposit of 2000, you can collect 121.80 in interest after two years.

5 0

2 years ago

Explain and show your work, please.

ArbitrLikvidat [17]

It is given that aiden has purchased a 2 lb package, a 3 lb package, and a 4 lb package
The first step is to add these packages together
2+3+4 is 9
each turkey burger needs 1/3 lb of turkey, which also means that every pound of turkey aiden has can make 3 turkey burgers

Aiden has 9 pounds of turkey, so he can make 27 turkey burgers (3*9)

Hope this helped! If you still need help I can answer in comments

5 0

3 years ago