Final answer:
To find the measurement of TS, you can use the Pythagorean theorem since TR is an altitude forming two right triangles. With TR=16 and RS=63, you calculate TS² = TR² + RS². Thus, the measurement of TS is 65 units.
Step-by-step explanation:
In the context provided, since TR is an altitude to triangle QTS, it divides triangle QTS into two right triangles. We are given that TR=16 and RS=63, and we are asked to find the measurement of TS. To solve for TS, we can apply the Pythagorean theorem to one of the right triangles formed by the altitude, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
If we name the point where the altitude meets TS as point U, the triangle formed by TRS is a right triangle with TR as one leg, RS as the other leg, and TS as the hypotenuse. Applying the Pythagorean theorem, we have:
TS² = TR² + RS²
TS² = 16² + 63²
TS² = 256 + 3969
TS² = 4225
To find TS, we take the square root of both sides:
TS = √4225
TS = 65
Therefore, the measurement of TS is 65 units.