The possible value of ∠V in the triangle is 86.8 degrees.
The angle of a triangle can be found using sine law.
To use the Law of Sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an angle opposite one of them (SSA).
Therefore, we know two sides and a angle.
let's find the ∠V using sine law.
In ΔTUV,
v = 77 cm
u = 72 cm
∠U = 69 degrees
Hence,
[tex]\frac{t}{sin T} = \frac{u}{sin U} = \frac{v}{sin V}[/tex]
72 / sin 69 = 77 / sin ∠U
cross multiply
72 sin ∠U = 77 sin 69°
sin ∠U = 77 sin 69° / 72
sin ∠U = 77 × 0.93358042649 / 72
sin ∠U = 71.8856928403 / 72
sin ∠U = 0.99841240056
∠U = sin⁻¹ 0.99841240056
∠U = 86.7710183817
Therefore,
∠U = 86.8 degrees.
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