Question

Compute the angle A if B= 81° 50' and C= 94°30' in a spherical triangle whose side c= 90°

Answer 1

spherical triangle....heard for 1st time...
sum of angles = 180 degrees, holds for this ?

Answer 2

180<(A+B+C)<540°

Answer 3

cool question :) Is this a triangle overlaid on a sphere? Like connecting New York, Dallas, and Seattle? I don't know if "sum of angles = 180" holds...

Answer 4

yeah. thats spherical trigonometry called sphaerica developed Menelaus' theorem.

Answer 5

sum of three vertex angles of a spherical triangle is greater than 180° and less than 540°
180<(A+B+C)<540°

Answer 6

u know law of sines for this ?

Answer 7

u can use that
sin a/sin A = sin b/sin B = sin c/sin C

Answer 8

oh, wait, 2 sides and one angle given, maybe law of cosines will help
cos A = - cos B.cos C + sin B.sin C.cos a

Answer 9

no side a given. how? :D

Answer 10

so u need cos a..hmm

Answer 11

there's no side b&c given to get cos a

Answer 12

i can think of this, .... find sin a in terms of sin A from sin law
find cos a in terms of cosA from cos law,
then square and add to eliminate 'a'

Answer 13

is that confusing ?

Answer 14

yeah.

Answer 15

just find sin a in terms of sinA from sin law...and tell me what u get

Answer 16

i dont get it. v.v

Answer 17

could u?
i m getting sin a =1.0031 sin A

Answer 18

sin a/ sin A = sin 90 / sin 94.5

Answer 19

ah..okay

Answer 20

so u get sin a =1.0031 sin A
now from cos law can u find cos a in terms of cos A ?

Answer 21

yup.

Answer 22

what u get ?