Question

Which ratio is equivalent to Sun U?

Answer 1

Answer:

  (a)  SV/VW

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides in a right triangle. This problem also makes use of the properties of similar triangles:

• corresponding sides are proportional
• corresponding angles are congruent

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sine ratio

The sine of angle U is given by ...

  Sin = Opposite/Hypotenuse

The side opposite angle U in ΔTUS is ST. The hypotenuse of that right triangle is side TU. This means the desired ratio is ...

  sin(U) = Opposite/Hypotenuse = ST/TU

corresponding ratio

In similar ΔVWS, angle W has the same measure as angle U. Its sine will be the ratio of the corresponding sides. The similarity statement ΔTUS~ΔVWS tells you that the side corresponding to ST is SV, and the side corresponding to TU is VW.

  sin(U) = sin(W) = SV/VW