Final answer:
To find the length of side T in triangle TUV, we calculate the third angle using the sum of angles in a triangle and then apply the Law of Sines with the given measurements to solve for side T.
Step-by-step explanation:
The student is asking to find the length of side T in a triangle labeled TUV given that side U is 75 cm (correcting the typo from 750 cm), angle T is 105°, and angle U is 42°. To solve this problem, we first need to find the length of side V, which can be done by employing the Law of Sines. Since we have one side and two angles known, we can calculate the third angle, angle V, using the fact that the sum of angles in a triangle is 180°. After finding angle V, we can then use the Law of Sines to find the length of side T.
First, let's find angle V:
180° - 105° - 42° = 33°
So, angle V = 33°.
Once we have all the angles, we use the Law of Sines:
(T/sin(105°)) = (75/sin(42°))
Now we solve for T:
T = 75 x (sin(105°)/sin(42°)
After calculating the above expression using a calculator, we round the result to the nearest centimeter to find the length of side T.