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3 years ago

Find c.

Mathematics

2 answers:

Greeley [361]3 years ago

7 0

9514 1404 393

Answer:

0.5 cm

Step-by-step explanation:

The Law of Sines tells you ...

c/sin(C) = b/sin(B)

c = b·sin(C)/sin(B)

c = (2 cm)sin(15°)/sin(105°) ≈ (2 cm)(0.2588/0.9659) ≈ 0.5359 cm

c ≈ 0.5 cm . . . . rounded to tenths

Vinvika [58]3 years ago

6 0

<h3>Answer: 0.5</h3>

========================================================

Explanation:

The ultimate goal is to find the value for lowercase c, or find the length of side c. So we'll use the portion sin(C)/c as part of the law of sines.

We don't know the value of lowercase 'a', so we'll ignore the sin(A)/a portion.

This leaves sin(B)/b

We see that one side is 2 cm long, so this means b = 2. The angle opposite this is 105 degrees, so B = 105.

The angle opposite side c is 15 degrees, so C = 15.

The lowercase letters represent side lengths, while the uppercase letters are angles.

--------------------------

We have enough to apply the law of sines to solve for side c.

sin(B)/b = sin(C)/c

sin(105)/2 = sin(15)/c

c*sin(105) = 2*sin(15) ............. cross multiply

c = 2*sin(15)/sin(105) .............. dividing both sides by sin(105)

c = 0.53589838486224

c = 0.5

Side c is roughly 0.5 cm long.

Make sure your calculator is in degree mode.

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