Question

find ae. round the answer to the nearest tenth.
a. 9.7
b. 13.5
c. 16.1
d. 17.3

Answer 1

@pitamar

Answer 2

Do you want guidance or the answer?

Answer 3

whichever

Answer 4

as long as its fast im fine with whichever

Answer 5

cuz im being timed

Answer 6

Do you know the law of cosines?

Answer 7

somewhat not reallly

Answer 8

$$a^2 + b^2 - 2ab \cos(\alpha) = c^2$$

Answer 9

it is an extension of the pythagorean theorem to all triangles, not just right angle triangles

Answer 10

somewhat not reallly

Answer 11

to use it, we have to figure out AB and angle ABE. we are told BE so that's all we need

Answer 12

to find AB we can use sin() function. can you find AB?

Answer 13

do i need a calculator?

Answer 14

31 degrres

Answer 15

we know that \(\sin( \angle ABC) = \frac{AC}{AB}\)

Answer 16

which becomes
$$\sin(31^\circ) = \frac{6}{AB}$$

Answer 17

can you solve this one for AB?

Answer 18

3.06?

Answer 19

arm.. let's just rearrange this. we can multiply both sides by AB:
$$ \sin(31^\circ) = \frac{6}{AB} \implies AB \cdot \sin(31^\circ) = 6 $$
and then divide by sin(31):
$$
AB = \frac{6}{\sin(31^\circ)}
$$calculating it I get 11.65

Answer 20

now the last thing we need is angle ABE. can you find it?

Answer 21

dont know how

Answer 22

we know that $$\angle CBA + \angle ABE + \angle EBD = 180^\circ $$
right? they all together make a flat angle.
We are told CBA and EBD. what are they?

Answer 23

31 and 13

Answer 24

Right, so we plug that in:
$$\angle CBA + \angle ABE + \angle EBD = 180^\circ \\
31^\circ + \angle ABE + 13^\circ = 180^\circ $$
Can you move the numbers to the right and find \( \angle ABE\)?

Answer 25

136? idk

Answer 26

yes, exactly

Answer 27

So, we know
$$
AB=11.65\\
BE = 7 \\
\angle ABE = 136^\circ
$$Now let's plug it in the formula. we'll say:
$$
a = AB = 11.65 \\
b = BE = 7 \\
\alpha = \angle ABE = 136^\circ
$$
and our formula is:
$$
c^2 = a^2 + b^2 - 2ab \cdot \cos(\alpha) \\
c^2 = (11.65)^2 + 7^2 - 2 \cdot(11.65) \cdot (7) \cdot \cos(136^\circ)
$$can you calculate this?

Answer 28

no ill get lost in them lol

Answer 29

cmon.. try

Answer 30

you can type it in here if you prefer:
http://www.wolframalpha.com/

Answer 31

idk how like ima forget all the numbers calculationg it

Answer 32

type
(11.65)^2 + 7^2 - 2*11.65*7*cos(136 degrees)

Answer 33

you see how it is actually the same expression? just textually. what do you get?

Answer 34

i got 302

Answer 35

correct
$$ c^2 = 302$$
we want \(c\) not \(c^2\) so we take root:
$$
c = \sqrt{302} = ?
$$

Answer 36

17.37

Answer 37

yep

Answer 38

thx!!

Answer 39

np
Just remember that in laws of cosines the angle has to be between the two sides you use, like we had in our case