Answer:
Angle R
Explanation:
RST is a triangle with sides RS = 11, RT = 9 and ST = 6.
To find the measure of the angles we need to use cosines law.
The cosines law is written as c² = a² + b² -2ab(cosC) where a,b,c are sides of the triangle and C is the angle opposed to side c.
- First we are going to find the angle RST using cosines law:
9²= 11²+6²-2(11)(6)(cosS)
81 = 121 + 36 -132cosS
81= 157 -132cosS
132cosS = 157 - 81
132cosS = 76
cosS = 76/132
cosS=.5757
S = 54.85
- Using the same method we're going to find the angle STR
11²= 6²+9²-2(6)(9)cosT
121= 36 + 81 -108cosT
121 = 117 -108cosT
108cosT= 117-121
cosT = -4/108
cosT = .0370
T= 87.88
- And finally solving for the angle SRT:
6²= 11² + 9² -2(11)(9)cosR
36 = 121 + 81 -198cosR
36 = 202 - 198cosR
198cosR = 202 -36
198cosR = 166
cosR = 166/198
cosR = 0.8383
R = 33.04
Therefore, we can conclude that the smallest measure is the one from angle R (∠SRT)