Given A 25 degree and b 10 choose four different values fo

Given A = 2.5 degree and b = 10, choose four different values for a so that (a) the information yields no triangle (b) the information yields exactly one right triangle (c) the information yields two distinct triangles (d) the information yields exactly one obtuse triangle

Solution

A = 2.5 deg and b = 10

use sine rule : a/sinA = b/sinB

sinB <=1 ; b*sinA/a<=1

a>=b*sinA = 10sin2.5 = 0.436 ; a= 0.2

So, b*sinA/a =0.436/0.2 = 2.18

So, a = 0.2 No traingle is possible

b) one right angled triangle : b*sinA/a = sinB = 1

b*sinA = a; a = 0.436

c) Two distinct traingles:

b*sinA/a<1
a> b*sinA > 10sin2.5 = 0.436 ; a = 0.5

sinB = 0.436/0.5 = 0.872

B 1= 60.69 ; B2 = 180 - 60.69 = 119.3 deg