Question

Can someone help me solve this problem?

Answer 1

Two Triangles are possible.

`color(brown)("Case 1 : " hat B = 60.6^@, hat C = 70.4^@, c = 162.3 " m"`
`color(orange)("Case 2 : " hat B = 119.4^@, hat C = 11.6^@, c = 34.6 " m"`

Explanation:

According to law of Sines,

`a / sin A = b / sin B = c / sin C`

Given : `a = 130 m, b = 150m , hat A = 49^@`

`sin B = (150 * sin 49) / 130 = 0.8708`

`hat B = sin ^-1 0.8708 = 60.6^@ " or " 119.4^@`

Hence, Two Triangles are possible.

Case 1 : `hat B = 60.6^@`

`hat C = 180 - hat A - hat B = 180 - 49 - 60.6 = 70.4^@`

`c = (a sin C) / sin A = (130 * sin 70.4) / sin 49 = 162.3 " m"`

Case 2 : `hat B = 119.4^@`

`hat C = 180 - hat A - hat B = 180 - 49 - 119.4 = 11.6^@`

`c = (a sin C) / sin A = (130 * sin 11.6) / sin 49 = 34.6 " m"`