Question

I need help with Geometry! This portfolio is due today and I have a question!

How do I know if I need to find the sine, cosine, or tangent of an angle? I know how to do all three I just don't understand which one I have to do. I'll attach my worksheet for examples of questions.

Answer 1

dear friend as regard to your number one question pythagoras theorem will be used to solve it because angle is not giving.whenever you are giving an angle or theta you can now use SOHCAHTOA

Answer 2

but which on do i use sin, cos, or tan?

Answer 3

for the rest of the problems..

Answer 4

Like question 4.

Answer 5

or 5..

Answer 6

Using sine, cosine, or tangent depends on which values are known and which values are unknown. Try filling in this chart:
Cosine relates the side ( opposite | adjacent ) to the angle, to the ___________, so I use cosine to solve problems where I know _____________ or ___________ and need the other one.
Sine relates the side ( opposite | adjacent ) to the angle, to the ___________, so I use sine to solve problems where I know _____________ or ___________ and need the other one.
Tangent relates the side ( opposite | adjacent ) to the angle, to the side ( opposite | adjacent ) so I use tangent to solve problems that do not involve the hypoteneuse.

Does that get you straight?

Answer 7

no.. i think im more confused.. can you use one of the problems like 4 and explain why it is the one it is?

Answer 8

for question 4
since we are looking for the opposite side we look for the formular that connects the opposite side and and any other side

Answer 9

now the only two that fit is TOA SOH

Answer 10

TOA wont work because it wont make opp the subject formular

SOH

Answer 11

what do you mean we are looking for the opposite side? How do you know that?

Answer 12

wait i think i get what you're saying.

Answer 13

BC is the opposite side

Answer 14

but i dont understand why you'd pick sin over tan?

Answer 15

to check your answer if it is correct use pythagoras to confirm if it will give you the same answer.\[\sin \theta=\frac{ opp }{ hyp}=\sin 32 \frac{ opp }{ 10.6 }=\sin32\times10.6=BC\]

Answer 16

that's not an answer choice

Answer 17

and i still dont understand why you picked sin over tan?

Answer 18

give me a sec

Answer 19

OK, #4: You know angle A, side AC ('adjacent' to A), and side AB (hypotenuse).
We are going to take baby-steps on the way to the answer.
Can you write two formulas with A=32°, that could solve for unknown BC?
Don't worry about whether the answers are in the list for #4 yet, just show me you know how to use the given dat afor a first try to find the answer.

Answer 20

sin(32)= BC/10.6 tan(32)=BC/8.2

Answer 21

Yes, good, you are using sine and tangent correctly. You may have noticed the two choices that use 32° are NOT correct math. Throw those out. And your two good choices are not on the list, so your teacher is messing with you to get you expand your thinking. So maybe 58° is important, but it is not in the figure! any ideas?

Answer 22

I have no idea.

Answer 23

I know how to use the formulas i just get confused on which one i have to use.

Answer 24

This is one of those problems that you mostly have to try all the answers to see if one is right. I can understand your confusion because three answer choices are WRONG math, so you don't learn much.
I have to go, but let me try this. the three angles inside a triangle add to 180°. We know one here is a right angle, 90°, so A and B add to 90°. A is 32° so B is 58° (90-32=58)
Change your perspective and write the formulas for angle B. Names change now.
AB is still the hypotenuse. AC is the side OPPOSITE angle B, and BC is the side ADJACENT.

So sine(B) = AC/AB. That is the one formula that will not help you solve the problem, so write out the other two.

Answer 25

So, not knowing which equation to use. It can be tough. Trial and error will help you learn how to choose. Identify what you DO know. See if you can fit it into one of the formulas. Remember, sine of an angle in a right triangle relates the side 'opposite' that is, the side not attached to that angle you are using and the hypotenuse.

Answer 26

this might help you figure out which to use
https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/intro-to-the-trig-ratios/v/basic-trigonometry

Answer 27

First idea: a right triangle has 3 sides, and we give them names.
The hypotenuse is the longest side. There is only one hypotenuse.
the name of the other two sides *depends on which angle we use*
so: pick an angle ( but *not* the 90 deg angle)
then label the sides opposite and adjacent (see video on how to do this)

Answer 28

2nd idea:
usually you know one side and want to find another side.
you also need to know an angle.

using the angle they give you, label all 3 sides.
then identify the two sides you will be using: 1 is known, the other you want to find
based on the "names" of those two sides, you will know to use sin, cos or tan

Answer 29

I understand what sine cosine and tangent are, i also know how to find them. My only problem is distinguishing which on to use to find the measurement I need. Can you please give me an example question? I attached my worksheet if you want to use one from there. That worksheet is due today and I'm so confused and don't know how to do it but I have to get it done.

Answer 30

There's a memory aid which you might find useful

SOH-CAH-TOA : -

Sine = Opposite / Hypotenuse

cos = Adjacent / Hypotenuse

tan = Opposite / Adjacent

Answer 31

@welshfella I already know that. I know how to find the sin, cos, tan of an angle i just don't know which one i have to use in different problems.

Answer 32

Look at your Problem 6. You are given two sides of the triangle. Using angle X, tell us the names of these two sides. That should tell you what formula to use for this problem. I think you just need confidence.

Answer 33

sine right? I think i get what you're saying!!!!

Answer 34

Yes, sine!
I hope you did the steps in-between!
The _opposite_side_ from X is 11, and the hypotenuse is 32.
sine = Opposite Over Hypotenuse, that's all it takes.
Go Forth And Conquer!

Answer 35

yep! so would the answer just be 11/32 or do i have to do something else?

Answer 36

write down what you know and what you need to find
take an example

Answer 37

x is the hypotenuse. 2 is opposite. the other is adjacent

Answer 38

angle = 30 . opp = 2 , hyp = x

you have OH therefore you need the sine

sin 30 = O/H = 2/x

Answer 39

Okay i get it thank you !

Answer 40

yw

Answer 41

I'm having trouble with number 4,5, 7, and 8. Could anyone help?

Answer 42

@mjdennis @welshfella

Answer 43

For #4, go back up and look at my other answers. It really is one where you should look at each answer and try to see if it is true in the formula, because 3 of them are just WRONG. Only one of the choices can be made using the information given.

Answer 44

im trying but its confusing me.. alot

Answer 45

SOHCAHTOA

Answer 46

which one are you doing ?

Answer 47

4.

Answer 48

#5, follow these steps:
First, understand the problem. See if the picture and problem match. Good.
Focus on the triangle. You know an angle and a side. You want to find the other side. You know nothing about the hypotenuse, but that should be OK; figure out which side is adjacent and which is opposite the angle, and write one of your formulas.

Answer 49

look at choice A:
sin 32 = BC/8.2

what are the "names" for BC and side 8.2 using angle 32 as the reference. any idea ?

Answer 50

i still dont know 4.

Answer 51

opp/adj

Answer 52

is sin opp/adj ?

Answer 53

no! cross off choice A

Answer 54

okay

Answer 55

Got it. I have to go. @phi is sharp and asking you the right questions. one step at a time!

Answer 56

okay thanks i really appreciate all your help

Answer 57

look at choice B
cos 32 = BC/10.6
what are the names for BC and side 10.6 ?

Answer 58

opp/hyp which is sin

Answer 59

so cross off choice B

Answer 60

and b says its cos.

Answer 61

tan would be BC/8.2, and it wouldnt b e58

Answer 62

and the last choice ?

Answer 63

for the last one the formula makes since but why does it say sin58, shouldnt it be sin 32?

Answer 64

for choice C, we have to be careful
tan 58 = 8.2/BC

notice they are using angle 58 (which is the unlabeled angle)
(the two angles 32+58 will always add up to 90)

anyway, when you use angle 58, the names change, the opposite side will be 8.2
and the adjacent side is BC

Answer 65

and yes, choice D would be correct if we used angle 32. But they are being sneaky and using the other angle (which is 58)
you know the unlabeled angle is 58 because it is 90-32

Answer 66

lost ?

Answer 67

so is it c? I get what your saying

Answer 68

yes, it is C

if we use angle 58, then side 8.2 is opposite and side BC is adjacent
do you see that ?

Answer 69

yes. Thanks. Now number 5.

Answer 70

this takes a small amount of thinking, and some trigonometry.

First, the trig.
in the triangle, what side do we know, and what side do we want to find ?

Answer 71

assuming we use angle 38 as the reference

Answer 72

adjacent

Answer 73

yes, we know adjacent.
what side do we want to find ?

Answer 74

t?

Answer 75

yes, we want to find how tall the tree is (the up/down direction)
if we know t and add 5 we will get the height of the tree.

Answer 76

that is the "thinking part"

Answer 77

what is the name for side "t" using 38 as the angle ?

Answer 78

opposite

Answer 79

we know adjacent (20) and want to find opposite. what should we use ?

Answer 80

tan?

Answer 81

yes TOA
tan = opp/adj
or , putting in numbers:

tan 38 = t/20

can you find t ?
I would first multiply both sides by 20

Answer 82

i dont think i can.?

Answer 83

this part is algebra.
\[ \frac{t}{20}= \tan 38 \\20 \cdot \frac{t}{20}= 20 \cdot \tan 38 \]
on the left side, that is the same as
\[ \frac{20}{20}t= 20 \cdot \tan 38 \]

Answer 84

what is 20/20 ?

Answer 85

the idea is anything divided by itself is 1, and 20 divided by 20 is 1
so you have
t = 20 * tan 38

you need a calculator to find t

Answer 86

ok