Answer:
22°
Step-by-step explanation:
To find the measure of angle T given all three side lengths of triangle RST, we can use the Law of Cosines:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Law of Cosines}}\\\\c^2=a^2+b^2-2ab \cos C\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a, b$ and $c$ are the sides.}\\\phantom{ww}\bullet\;\textsf{$C$ is the angle opposite side $c$.}\end{array}}[/tex]
In this case, the angle we wish to find is angle T, so:
Therefore:
[tex]RS^2=ST^2+TR^2-2(ST)(TR)\cos T[/tex]
Given that RS = 3 cm, ST = 5 cm and RT = 7cm , substitute these values into the equation and solve for T:
[tex]3^2=5^2+7^2-2(5)(7)\cos T \\\\\\9=25+49-70\cos T \\\\\\9=74-70\cos T \\\\\\70\cos T=74-9 \\\\\\70\cos T=65 \\\\\\\cos T = \dfrac{65}{70} \\\\\\T=\cos^{-1}\left(\dfrac{65}{70}\right) \\\\\\T = 21.7867892982...^{\circ} \\\\\\T=22^{\circ}[/tex]
Therefore, the measure of angle T rounded to the nearest degree is:
[tex]\LARGE\boxed{\boxed{22^{\circ}}}[/tex]
