Question

Geometry: Find the missing parts of the triangle.(Picture in below post)

Answer 1

where's the pic??

Answer 2

sorry slow computer

Answer 3

i know i need to use the law of cosines, i just cant figure out how

Answer 4

are you being asked to find "f"?

Answer 5

yeah and the other missisng parts

Answer 6

the angles??

Answer 7

yep

Answer 8

i know we have to start by finding f

Answer 9

can you write down the Law of Cosines?

Answer 10

yes

Answer 11

write it down.

Answer 12

\[a ^{2}=b ^{2}+c ^{2}-2bc(Cos(A))\]

Answer 13

the "unknown" is side a in your formula. side a is opposite angle A

I would find the angle that corresponds to angle A
and the lengths of the sides "next to" to angle A (these will be b and c)
can you do that ?

Answer 14

i think

Answer 15

so a would be f right

Answer 16

i had a hard time balancing the equation for some reason...

Answer 17

if we match up side "f" with "a"
then we need the angle across from side f to be angle A

Answer 18

ok

Answer 19

so \[a ^2 = 169(\cos(A))\]

Answer 20

you left out a few things. We start with
\[ a ^{2}=b ^{2}+c ^{2}-2bc(Cos(A)) \]
the first thing is match up these letters with your problem
you matched "a" with side f
the angle A is the angle opposite side f. What is the measure of that angle ?

Answer 21

87

Answer 22

so then a=2.974

Answer 23

radian, of course

Answer 24

yes angle C is 87
so far we have
f^2 = b^2 + c^2 - 2 b c cos(87)

b and c are the known sides (that form the angle at 87)
which is which does not matter. so let b= 15 and c= 28

Answer 25

I would not bother changing to radians (unless your calculator does not do degrees.. but I'ms sure it does)

Answer 26

ok, so then substitute the variables

Answer 27

f^2=225+784-2(15)(28) cos(A)

Answer 28

f^2=1009-840cos(A)

Answer 29

don't forget to also replace A with 87º

Answer 30

ok

Answer 31

so a = 2.974

Answer 32

that doesnt make sense

Answer 33

what did you do. Is your calculator in degree mode? what did you get for cos(87º) ?

Answer 34

you should be doing
f^2=1009-840cos(87)

Answer 35

yeah and i got .05233

Answer 36

so you now have
f^2=1009-840*.05233

Answer 37

ohh it was in radial i think....

Answer 38

oh! that fixed it... f is 9.813

Answer 39

no. what is
1009-840*.05233

Answer 40

8.4337

Answer 41

I assume you know you do multiplies before addition, right?

Answer 42

ohhhhhhhhh. ordeer of op.

Answer 43

riigght

Answer 44

so f^=965.0428

Answer 45

yes. now take the square root

Answer 46

so f= 31.065

Answer 47

now you have all 3 sides and 1 angle.
to find an angle, use the Law of Sines

Answer 48

sometimes i forget the simplist things.. like 3 grade maths -_-

Answer 49

ok thanks

Answer 50

i an much more comfortable with law of sines

Answer 51

what do you get for angle H ?

Answer 52

um so 87/31.065=h/15

Answer 53

cross multiply and h is 42.01

Answer 54

the law of sines does use sin!

Answer 55

oops

Answer 56

darn

Answer 57

so instead of the angle, you should use sin(angle) in your ratios

Answer 58

so in THAT case, h = 28.828

Answer 59

yes, angle H is 28.83º (rounded to 2 decimal places)

Answer 60

and if that is true then we just add up the kmown angles and thes subtract that from 180 for the 3 angle.

Answer 61

thank you SO MUCH!

Answer 62

or use the Law of Sines a second time. (though your way is easier)

Answer 63

ok :) i try to do the least ammount of work possible, lol

Answer 64

yes, a good strategy. But now you can do the Law of Sines and check your answer against the number you get the other way.

Answer 65

ok.