Answer:
∠TSR= 48°
∠RTS = 107°
∠TRS = 25°
Step-by-step explanation:
As we know in any triangles,
- a, b and c are sides
- C is the angle opposite side c
We can apply The Law of Cosines , which is:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] − 2ab cos(C)
In this situation we have:
- RT = a = 11
- TS = b = 6
- SR = c = 14
Apply The Law of Cosines to find the angle of TRS
<=> [tex]6^{2} = 11^{2} + 14^{2} - 2*11*14*cos(TRS)[/tex]
<=> cos(TRS ) = ([tex]11^{2} + 14^{2} - 6^{2}[/tex]) / 2*11*14
<=> cos(TRS ) = 0.91
<=> ∠TRS = 25°
Apply The Law of Cosines to find the angle of RTS
<=> [tex]14^{2} = 11^{2} + 6^{2} - 2*11*6*cos(RTS)[/tex]
<=> cos(RTS) = ([tex]11^{2} + 6^{2} - 14^{2}[/tex]) / 2*11*6
<=> cos(RTS) = -0.29
<=> ∠RTS = = 107°
So we can find the measure of angle TSR
∠TSR= 180° - 107° - 25°
∠TSR= 48°
