Answer :
The measure of the angle ∠V is 80 degrees then the side length of the triangle t is 3.26 cm.
What is trigonometry?
Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
In ΔTUV, v = 4.9 cm, ∠T=41° and ∠U=59°.
We know that the sum of all the angles of the triangle is equal to 180 degrees. Then the angle ∠V will be
∠T + ∠U + ∠V = 180
41 + 59 + ∠V = 180
∠V = 80
Then by the sine rule, we have
[tex]\dfrac{t}{\sin T} = \dfrac{u}{\sin U} = \dfrac{v}{\sin V}\\\\\dfrac{t}{\sin 41} = \dfrac{u}{\sin 59} = \dfrac{4.9}{\sin 80}[/tex]
Then consider the first and the third terms, then we have
[tex]\begin{aligned} \dfrac{t}{\sin 41} &= \dfrac{4.9}{\sin 80}\\\\t &= 3.26\end{aligned}[/tex]
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ2