In DeltaSTU,t=77 inches, s=22 inches and /_S=161^(@). Find all possible values of /_T, to the nearest degree. Answer:

Apply Law of Sines: To find the possible values of angle T, we can use the Law of Sines, which relates the sides of a triangle to the sines of its opposite angles. The Law of Sines states that for any triangle ABC with sides a, b, and c opposite angles A, B, and C respectively, the following ratio holds true: (sin A)/a = (sin B)/b = (sin C)/c. We will apply this to triangle STU.Find sine of angle S: First, we need to find the sine of angle S. Since angle S is given as 161 degrees, we can calculate its sine using a calculator. sin(161°) ≈ 0.46947156Set up ratio for sides: Now, we can set up the ratio using the Law of Sines for sides s and t and their opposite angles S and T respectively. (sin S)/s = (sin T)/t Substituting the known values, we get: (sin 161°)/22 = (sin T)/77Solve for sin T: Next, we solve for sin T by cross-multiplying. sin T = (sin 161°) * (77/22) sin T ≈ 0.46947156 * (77/22) sin T ≈ 1.651

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In
DeltaSTU,t=77 inches,
s=22 inches and
/_S=161^(@). Find all possible values of
/_T, to the nearest degree.
Answer:

In $\Delta \mathrm{STU}, t=77$ inches, $s=22$ inches and $\angle \mathrm{S}=161^{\circ}$ . Find all possible values of $\angle \mathrm{T}$ , to the nearest degree. $\newline$ Answer:

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Q. In

\Delta \mathrm{STU}, t=77

inches,

s=22

inches and

\angle \mathrm{S}=161^{\circ}

. Find all possible values of

\angle \mathrm{T}

, to the nearest degree.

\newline

Answer:

Apply Law of Sines: To find the possible values of angle $T$ , we can use the Law of Sines, which relates the sides of a triangle to the sines of its opposite angles. The Law of Sines states that for any triangle $ABC$ with sides $a$ , $b$ , and $c$ opposite angles $A$ , $B$ , and $C$ respectively, the following ratio holds true: $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ . We will apply this to triangle $STU$ .
Find sine of angle S: First, we need to find the sine of angle S. Since angle S is given as $161$ degrees, we can calculate its sine using a calculator. $\newline$ $\sin(161^\circ) \approx 0.46947156$
Set up ratio for sides: Now, we can set up the ratio using the Law of Sines for sides $s$ and $t$ and their opposite angles $S$ and $T$ respectively. $\frac{\sin S}{s} = \frac{\sin T}{t}$ Substituting the known values, we get: $\frac{\sin 161°}{22} = \frac{\sin T}{77}$
Solve for $\sin T$ : Next, we solve for $\sin T$ by cross-multiplying. $\sin T = (\sin 161°) \cdot (\frac{77}{22})$ $\sin T \approx 0.46947156 \cdot (\frac{77}{22})$ $\sin T \approx 1.651$