Find all possible solutions if any for delta ABC Round all s

Find all possible solutions, if any, for delta ABC, Round all side lenghts to the nearest tength and all angle measures to the nearest tength of a degree. Clearly indicate your final answer. A = 42 degrees, B = 59 degrees, b = 23 Circle all of the statements that are true about right triangles delta ABC and delta DEC. Given: delta ABC - delta DEC A = D tan A = cot ECD sec ACB = csc D sin CAB = cos DCE

Solution

(21)

a/sinA = b/sinB

2/sin30 = 3/sinB

2/0.5 = 3/sinB

4 =3/sinB

sinB = 3/4

B = sin ^-1(3/4)

B = 48.6^o

hence, A+B+C=180

30+48.6+C=180

78.6+C=180

C =101.4^o

finding c,

b/sinB= c/sinC

3/0.75 = c/sin(101.4)

4= c/sin(101.4)

c= 4*sin(101.4)

c= 4*0.76

c = 3.04

(22)

B E

A D

ACB ECD

in triangle ABC

we have,

A+B+C= 180

A+90+C = 180

A+C = 90

A=90 - C ..(i)

tan A = cot ACB

tan A = cot ECD

from (i),we have

A=90-C

sin CAB = Sin 90-ACB

sin CAB = cos ACB

sin ACB = cos DCE