Question

In the triangle below, determine the value of a.

http://static.k12.com/eli/bb/817/-1/0/2_37302_44974/-1/b0c7bc40f7e5f494498c3168c8648c065cd7076e/media/07512d1f21d60f725c1203d778161bab63f9449d/mediaasset_651981_1.png

Answer 1

I would just like to know how to set this up.

Answer 2

@phi @paki anyone?

Answer 3

@ash2326 @tkhunny

Answer 4

do you know SOH CAH TOA ?

Answer 5

Kind of. I know what they stand for but not how to use them.

Answer 6

the basics of trig are given by
http://www.khanacademy.org/math/trigonometry/basic-trigonometry/basic_trig_ratios/v/basic-trigonometry

Answer 7

when you have time, you can look at that and the following video.

in the mean time, you have a right triangle with 3 sides.

Answer 8

yup thats an awesome link

Answer 9

pick one of the angles (but not the right angle)

in this problem, pick the angle we know (the one labeled 42º)

Answer 10

Ok

Answer 11

once you have picked the angle, label the 3 sides

one of the sides is always the same name , the hypotenuse
do you know which side is the hypotenuse?

Answer 12

Side AC

Answer 13

one side is "opposite" angle 42º
which side is opposite ?

Answer 14

Side CB

Answer 15

opposite is the side you see if you "stand" at the angle (labeled 42 in this case) and look out and across.

yes side CB

and that leaves the 3rd side as "adjacent" (adjacent means "next to" , and we use that name because that side is "next to" the angle (in some sense)

Answer 16

until this is totally obvious, you should label the 3 sides (based on using angle 42)
hyp, opp, and adj.

Answer 17

Which is side AB

Answer 18

we now look at the problem.
we want to find at least 2 (out of the 3) sides that are "interesting"

what makes a side interesting?
1) it's a side we want to "solve for"
2) it's a side we know the length of.

in this case we have 2 interesting sides. What are their "names" (i.e. which are they out of hyp, opp, and adj )

Answer 19

Sides CB and AB I believe

Answer 20

and just as important, what are their names?

Answer 21

AB is Adjacent and CB is opposite

Answer 22

ok, now we are ready to use SOH CAH TOA

we look for the "trio" that uses adjacent and opposite. which one ?

Answer 23

Tan or TOA

Answer 24

yes.

TOA is a mnemonic (memory aid) for tan(angle) = opposite / adjacent

now fill in angle (with 42º) , opposite (with a) and adjacent with 14

Answer 25

OK

Answer 26

what do you have after you fill in the info?

Answer 27

Tan= a/14?

Answer 28

This is what I was confused about I don't really understand what I'm supposed to be putting into my equation to solve the question with.

Answer 29

almost. remember tan (and sin and cos) take an "argument"
For example, you may have learned sin(30º) = ½ (you can test that on a calculator)
you give the sin an angle and it returns a number

in this case, you have tan of the angle we used when we labeled the sides.

in other words,
tan(42) = a/14

Answer 30

the next step is use algebra. multiply both sides by 14
\[ 14 \tan(42º) = \frac{a}{14} \cdot 14 \]
on the right side 14/14 is 1 and we have
\[ 14 \tan(42º) = a\]
or
\[ a= 14 \tan(42º) \]

Answer 31

Ahhhh so 32.08 then?

Answer 32

be sure your calculator is in *degree mode*

Answer 33

How do I do that with a graphing calc.?

Answer 34

which calculator do you have?

Answer 35

A TI-84

Answer 36

And it wouldn't be 32.08 then?

Answer 37

no, because your calculator is interpreting the 42 as 42 radians

Answer 38

I tried it with my phone's calculator and got 12.6 would that be correct?

Answer 39

yes, 12.6

I just downloaded the TI-84 manual and looked at it.
It says press the "mode" button

Answer 40

you should get a list of settings

Answer 41

It says it is in degrees mode?

Answer 42

Oh nevermind

Answer 43

use the arrow button to move down to degree/radian line
and use the sideways arrow to select degrees

Answer 44

Could I have you check my answer on another one of these to be sure i'm doing it right?

Answer 45

And thank you for the help.

Answer 46

ok, but make it a new post, please

Answer 47

Sure just a sec.