Trigonometric ratios in right triangles Problem

Find \sin(\alpha)sin(α)sine, left parenthesis, alpha, right parenthesis in the triangle.

Choose 1

Choose 1

(Choice A)

A

\dfrac{12}{35}

35

12



start fraction, 12, divided by, 35, end fraction

(Choice B)

B

\dfrac{12}{37}

37

12



start fraction, 12, divided by, 37, end fraction

(Choice C)

C

\dfrac{35}{12}

12

35



start fraction, 35, divided by, 12, end fraction

(Choice D)

D

\dfrac{35}{37}

37

35

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

/

step-by-step explanation:

the bolded word " farsighted" could be replaced with visionary.

the answer is b.

64

step-by-step explanation:

c=2πr=2·π·8≈64