All categories

2 years ago

In triangle ABC, a = 9, c = 5, and B = 120°. Find b^2

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

6 0

We can find b by using the cosine rule of a triangle.

$b^2=a^2+c^2-2ac CosB$

First step is to plug in the given values in the above equation. So,

$b^2=9^2+5^2-2*9*5*Cos (120)$

$b^2=81+25-90(-\frac{1}{2} )$

=106+45

=151

So, b^2=151

You might be interested in

The diagram above shows a rectangle inscribed in a circle AB=10 and AC =12 caculate the total surface area of the shaded part

erastova [34]

Answer:

$71.63 \: \: \mathrm{cm^2 }$

Step-by-step explanation:

Once we know the diameter of the circle, we can figure out the problem.

The diameter of the circle = The diagonal of the rectangle inscribed in the circle

To find the diagonal of the rectangle, we can use a formula.

$d=\sqrt{w^2 + l^2}$

The width is 10 cm and the length is 12 cm.

$d=\sqrt{10^2 + 12^2}$

$d \approx 15.62$

The diagonal of the rectangle inscribed in the circle is 15.62 cm.

The diameter of the circle is 15.62 cm.

Find the area of the whole circle.

$A=\pi r^2$

The $r$ is the radius of the circle, to find radius from diameter we can divide the value by 2.

$r = \frac{d}{2}$

$r=\frac{15.62}{2}$

$r=7.81$

Let’s find the area now.

$A=\pi (7.81)^2$

$A \approx 191.625$

Find the area of rectangle.

$A=lw$

Length × Width.

$A = 12 \times 10$

$A=120$

Subtract the area of the whole circle with the area of rectangle to find area of shaded part.

$191.625-120$

$71.625 \approx 71.63$

5 0

2 years ago

This is big ideas work pls show how u do it so i know

Komok [63]

Answer:

(5,-1)

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer be

olasank [31]

Hello,

$u_{1} =4\\
 u_{2} =4*q\\
 u_{3} =4*q^2\\
...\\

 u_{9} =4*q^8\\\\
==\textgreater\ 4*q^8=1024\\
==\textgreater\ q^8=256\\
==\textgreater\ q=2\mbox{( and there is a problem in the question) } \ or \ q=-2\\
if\ q=2 \ then\ \sum_{i=0}^{8}\ 4*(2)^i= 4*\dfrac{1-2^9}{1-2} =2044\\

if \ q=-2 \ then\ \sum_{i=0}^{8}\ 4*(-2)^i= 4*\dfrac{1-(-2)^9}{1+2} =684\\



$

Answer B (but see the problem)

7 0

2 years ago

Read 2 more answers

I don't know how do do it can u help me

Blizzard [7]

Answer:

The second regon

Step-by-step explanation:

4 0

2 years ago

one day in october, agent sanchez enters the code 3477 how do you know this is code is incorrect and and will not open the door

kozerog [31]

Well first off the cia will say that they didn’t send him, but we know the truth. Second off that number is the last 4 digits to the illuminatis president, Tom Hanks. Lastly, that number is also the number of kids Joe Biden has sniffed in the last year.

5 0

2 years ago