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1 year ago

If m∠A = 56°, m∠B = 60°, and c = 8, what is the measure of side length b?

Mathematics

1 answer:

Alekssandra [29.7K]1 year ago

5 0

Using the law of sines:

$\frac{b}{sin(B)}=\frac{c}{sin(C)}$

Solve for b:

$\begin{gathered} b=\frac{c\cdot sin(B)}{sin(C)} \\ so: \\ b=\frac{8\cdot sin(60)}{sin(64)} \\ b\approx7.708 \end{gathered}$

Answer:

7.708

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In-s [12.5K]

If you only want to see the way i do it to get the answer without seeing my explanation ignore sentences with symbol '#'

<h2>Answer</h2>

•Pic on the left

x = 8.36

y = 140.18°

• Pic on the right

x = 110°

• This one for the pic on the left

#Since the total degree of a triangle is 180° and one of the side known 90° (L) so the rest must be 90° (180° - 90° = 90°)

#known that the other side of triangle degree is (5x - 2)° and 6x° so... u can find the x! :D

90 = (5x - 2) + 6x

90 = 11x - 2

90 + 2 = 11x

92 = 11x

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x = 8.36 (2 decimal places)

#Now you know the x, you can now find the degree

#degree of (5x - 2)

5x - 2 =

5(8.36) - 2 =

41.81 - 2 = 39.81

#Since the y° is in the other side of the line of degre 39.81°, you can find it by minus it with 180° (straight line with no degree is 180°)

180° - 39.81° = 140.18

•This one for the pic on the right

#Lol this one is easy. I already told you before that the straight line degree is 180° and you can find one of the side if you know one of the degree side, so you can find it.

# Also as i said before, total triangle degree is 360°

#Find the degree of the other side of x° (only can find the degree of other side x because its inside the triangle)

Degree = 180° - 80° - 30° = 70°

#Now you can get x

x = 180° - 70° = 110°

<h2>For moderators that see this</h2>

#Moderators please don't be mean, dont delete my answers just for approval from your senior or just to get the biggest moderation daily rank. This answer is long, how can you just instanly delete it? :(

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