Final answer:
The sine of ∠U in right-angled triangle ∆TUV is the ratio of the length of the opposite side to the length of the hypotenuse, which is 7/25.
Step-by-step explanation:
The student is asking about a trigonometric ratio in a right-angled triangle. In a right-angled triangle ∆TUV, where ∠V is a right angle (90°), VU (which can be considered as the opposite side with respect to ∠U) is 7 units, UT (which is the hypotenuse in this context) is 25 units, and TV (which can be considered as the adjacent side with respect to ∠U) is 24 units. The sine of ∠U is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Thus, the sine of ∠U can be calculated as sine(∠U) = opposite/hypotenuse = VU/UT = 7/25.
To find the ratio that represents the sine of angle U in triangle TUV, we need to first find the length of the side opposite angle U (which is VT) and the hypotenuse of the triangle (which is TU). Then we can use the formula sine(angle) = opposite/hypotenuse to find the sine of angle U.Step 1: Find VT using Pythagorean Theorem: VT^2 = TU^2 - TV^2, VT^2 = 25^2 - 24^2, VT^2 = 625 - 576, VT^2 = 49, VT = √49, VT = 7.Step 2: Use the formula sine(U) = VT/TU, sine(U) = 7/25. The ratio that represents the sine of angle U is 7/25.