Question

In triangle DEF, angle D = 44 degrees, angle E = 61 degrees, and segment EF = 20 inches. What is the length of segment DE?

Answer 1

So you can add the two angles together then subtract by 180 first

Answer 2

angle f = 75

Answer 3

Then do law of sines.

Answer 4

Laws of sines.
You have the angle D (opposite to EF), just discover the angle F (opposite to DE).
44 + 61 + angle F = 180
angle F= 180-44-61 = 75

Now, laws of sines:
EF/sin44º = ED/sin75º

Answer 5

so sin44/20=sin75/DE

Answer 6

sin44/20 = .
035, sin75/de = .035

Answer 7

Just solve for DE.

Answer 8

DE = sin75 x sin44/20?

Answer 9

No, DE = 20*sin75/sin44

Answer 10

27.8

Answer 11

Yes.

Answer 12

A cruise ship travels 300 miles east, then turns 30 degrees north, and travels another 175 miles. What is the total distance from its starting point?

Answer 13

Laws of cosines. You have 2 sides and the angle between this sides. Just use the formula that I said to you yesterday:
c² = a² + b² - 2abcos theta

c is the side that you want to discover opposite to the angle theta.

Answer 14

172 miles

Answer 15

yes yes

Answer 16

In triangle XYZ, XY = 15, YZ = 21, and XZ = 27. What is the measure of angle Z to the nearest degree?

Answer 17

xy is opposite of angle Z

Answer 18

XZ is hypotenuse, YZ is adjacent

Answer 19

the triangle is right ?

Answer 20

i don't know, there's no picture or diagram

Answer 21

So you can't that there's a hypotenuse rs.

Answer 22

cant say*

Answer 23

oh, okay. i just assumed the hypotenuse was XZ because it's the longest segment

Answer 24

you have to use the other laws of cosine formula.
Cos theta = (a² + b² - c²) / ( 2*a*b)

Answer 25

c is the side opposite to the angle that you want.

Answer 26

so XY is my c

Answer 27

yep

Answer 28

i got 89.9 but that's not an option

Answer 29

are you sure?
cos theta = (27² + 21² - 15² )/2*27*21 = 0.83

Answer 30

do arccos with 0.83

Answer 31

33.9 which rounds up to 34

Answer 32

there's an option?

Answer 33

yep! 34 is an option

Answer 34

:)

Answer 35

verify the identity:

http://puu.sh/3e9qD.png

Answer 36

It's to say that it's true or false?

Answer 37

Or re-do the identity ?

Answer 38

i have to show the steps of verifying that it is true or false

Answer 39

Ok, okay,

Answer 40

a minute

Answer 41

I got it, i will write in latex.

Answer 42

\[\frac{ \sec x }{ \csc x - \cot x } - \frac{ \sec x }{ \csc x + \cot x } = \frac{ \sec x (\csc x + \cot x) - \sec x (\csc x - \cot x) }{ \csc²x - \cot²x }\]
\[\csc² x - \cot ²x = 1\]

So, we will have,
\[\sec x(\csc x + \cot x) - \sec x (\csc x - \cot x) =\] \[\sec x \csc x + \sec x \cot x - \sec x \csc x + \sec x \cot x\]\[2\sec x \cot x = 2 \frac{ 1 }{ \cos x } * \frac{ 1 }{ \tan x } = 2 \frac{ 1 }{ \cos x } * \frac{ \cos x }{ sen x } = \]\[2*\frac{ 1 }{ sen x } = 2\csc x\]

Answer 43

If you don't get it, i will try to explain better.

Answer 44

i get it. thank you so much.

Answer 45

Just to make it complete, I said that csc²x - cot²x = 1 because:
\[\csc² x = \frac{ 1 }{ sen² x } \iff \cot² x = \frac{ \cos² x }{ sen² x }\]\[\csc² x - \cot² x = \frac{ 1 }{ sen² x } - \frac{ \cos² x }{ sen² x } = \frac{ 1- \cos² x }{ sen x }\]But you now that \[sen² x + \cos² x = 1\]So,\[sen²x = 1 - \cos²x\]To conclude,\[\csc²x - \cot²x = \frac{ 1 - \cos²x }{ sen²x } = \frac{ sen²x }{ sen²x } = 1\]