The hypotenuse of a 30 -60 -90 triangle is 13cm. What is the length of the shorter leg?

Mathematics

1 answer:

Ivahew [28]3 years ago

6 0

Answer:

(13/2) cm

Step-by-step explanation:

The hypotenuse here is of length 13 cm. The shorter leg lies opposite to the 30° angle. Recall that the sine function is defined as

opposite side

sin Ф = -----------------------

hypotenuse

which, in this case, works out to:

opposite side

sin 30° = -----------------------

13 cm

and so the length of the opposite side (which is also the "shorter leg") is

shorter leg length = (13 cm)(sin 30°) = (13 cm)(1/2) = (13/2) cm

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