Use the Law of Sines and/or the Law of Cosines to solve each triangle. Round to the Nearest tenth when necessary

(Unit 8: Right Triangles & Trigonometry, Homework 9: Law of Sines & Cosines: + Applications)

∠TSR= 48°

∠RTS = 107°  

∠TRS = 25°

Step-by-step explanation:

As we know in any triangles,

We can apply The Law of Cosines , which is:

= +  − 2ab cos(C)

In this situation we have:

Apply The Law of Cosines to find the angle of TRS

<=>

<=> cos(TRS ) = () / 2*11*14

<=> cos(TRS ) = 0.91

<=> ∠TRS  = 25°

Apply The Law of Cosines to find the angle of RTS

<=>

<=> cos(RTS) =  () / 2*11*6

<=> cos(RTS) = -0.29

<=> ∠RTS = = 107°  

So we can find the measure of angle TSR

∠TSR= 180° - 107°  - 25°

∠TSR= 48°

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.