Question

An obtuse triangle has angle measurements of 100°, 60°, and 20°. If the longest side of this triangle is 20 feet, what is the length of its shortest side, s?

Answer 1

Have you heard about the law of sines?

Answer 2

yes @johnweldon1993

Answer 3

Cool because I didnt know how to go about this if you didnt lol

Okay so we know

\[\large \frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}\]

Answer 4

lol okay @johnweldon1993

Answer 5

So we have the side of 20 ft....and the angle that faces it is 100 degrees right?

And we have the angle that faces the 's' side that we want is the 20 degrees right?

Answer 6

right. @johnweldon1993

Answer 7

So we can set up our law of sines to be

\[\large \frac{sin(100)}{20} = \frac{sin(20)}{s}\]

and solve for 's'

Answer 8

okay i think i got it, for this problem i got 6.9 ft is that correct? @johnweldon1993

Answer 9

*shouldda calculated it huh*

...yeah 6.9 is correct :)

Answer 10

okay thanks! :-) could you help me with another one? @johnweldone1993 please

Answer 11

Oh god another one????? >.< haha no jk of course :P

Answer 12

haha thanks, okay so
ABCD is a parallelogram. Its diagonal, AC, is 18 inches long and forms a 20° angle with the base of the parallelogram. Angle ABC is 130°. What is the length of the parallelogram’s base, AB?

Answer 13

@johnweldon1993

Answer 14

Hint. what do all the angles in any triangle add up to?

Answer 15

360?? @johnweldon1993

Answer 16

Not quite...that is a circle :)

the interior angles of a triangle ALWAYS add up to 180 degrees okay?

So here...focus on the lower triangle

Answer 17

So to solve for that angle labeled ?? right now

We know those 3 angles will add to make 180...so if we already have 20...and 130....what would the other angle be?

Answer 18

OHHHHH. crap sorry for some reason i was thinking of a square. and yes so 30?? @johnweldon1993

Answer 19

Lol no problem :)

and yes 30 good...so we have



now we just have the law of sines again :)

we have the angle 30 facing that side we need

and we have the angle 130 facing the 18 we have so

\[\large \frac{sin(130)}{18} = \frac{sin(30)}{b}\]

and solve for 'b'