Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
B = 40°, b = 25, c = 26

Answer 1

@campbell_st

Answer 2

yep... 1 triangle will have an angle C as an acute angle, an the other will have angle C as an obtuse angle.

Answer 3

Okay this one is tough... I need the values of A C and a on the first triangle, and A C and a on the second one

Answer 4

get one first

Answer 5

Idk what to do, like, at all

Answer 6

well, you do know the Law of Sines, right?

Answer 7

a/sinA = b/sinB = c/sinC

Answer 8

right, so use the "b" and "B" values and "c" given using the part
b/sinB = c/sinC

Answer 9

sinB/b = sinC/c either way, you can flip them around btw

Answer 10

a/sinA = 25/sin40 = 26/sinC

Answer 11

yes, the idea is that you may not have all 3 at once, just a pair, so you use just one pair at a time :)

Answer 12

so just use 25/sin40 = 26/sinC

Answer 13

so, what do you get for the sinC?

Answer 14

Im trying but idk how to do it

Answer 15

well, at
25/b = 26/c
how would you solve for "c"?

Answer 16

move the left to the right?

Answer 17

here is the 1st case

\[\frac{Sin(40)}{25} = \frac{\sin(C)}{26} \]

solve for C

C = 41.95 degrees

and you also need to consider the case when

C = 180 - 41.95

so

C = 138.05 degrees.

Answer 18

find angle A by angle sum of a triangle when you know the values of angle C

Answer 19

A = 98.05?

Answer 20

the other A = 1.95?

Answer 21

well that seems to work.

Answer 22

but then how do i get a?

Answer 23

well if you need a

then

\[\frac{25}{\sin(40)} = \frac{a}{\sin(98.05)}..... and ..... \frac{25}{\sin(40)} = \frac{a}{\sin(1.95)}\]

solve for a. each triangle will have a different value for a.

in the 1st case a will be larger than 26

in the 2nd triangle a will be very small...
hope this helps.

Answer 24

It helps a whole lot man. Thank u so much camp!

Answer 25

A = 98°, C = 42°, a = 38.5; A = 2°, C = 138°, a = 1.4