Question

Can someone please explain to me how to get this answer?

Answer 1

Answer:

33,2 ≈ c

45 ≈ b

120° = A

Step-by-step explanation:

We will be using the Law of Sines:

Solving for Angle Measures

$\frac{ \sin∠C}{c} = \frac{ \sin∠B }{b} = \frac{ \sin∠A}{a}$

** In the end, use the sin⁻¹ function or else you will throw off your answer.

Solving for Sides

$\frac{c}{ \sin∠C} = \frac{b}{ \sin∠B} = \frac{a}{ \sin∠A}$

Given instructions:

• 68 = a
• 25° = C
• 35° = B

Well, the first thing we can do is to find the m∠A, and we have to use the Triangular Interior Angles Theorem:

25° + 35° + m∠A = 180°

|________|

60° + m∠A = 180°

-60° - 60°

__________________

m∠A = 120°

Now that we have the third angle measure, we can use it in the formula to find the other sides of the triangle, like side c:

$\frac{c}{ \sin 25°} = \frac{68}{ \sin 120°} \\ \\ \frac{68 \sin 25°}{ \sin 120°} ≈ 33,18383234 ≈ 33,2 \\ \\ 33,2 ≈ c$

Now, we have to find side b:

$\frac{b}{ \sin 35°} = \frac{68}{ \sin 120°} \\ \\ \frac{68 \sin 35° }{ \sin 120° } ≈ 45,03701335 ≈ 45 \\ \\ 45 ≈ b$

Now everything has been defined!

I am joyous to assist you anytime.

Answer 2

Answers:
A = 120
b = 45.0
c = 33.2

Side Note: only one triangle is possible
See attached for a visual. I used GeoGebra to draw the triangle.

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Explanation:

We are given the following information
B = 35
C = 25
a = 68

We need to find the following
A, b, c

where the lower case letters represent the side lengths; the upper case letters are the angles. The angles are opposite their corresponding sides. For instance, side lowercase b is opposite angle uppercase B. The other letters are positioned the same way.

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First use the idea that for any triangle, the three angles (A,B,C) must add to 180 degrees
A+B+C = 180
Replace B and C with 35 and 25. Solve for angle A
A+35+25 = 180
A+60 = 180
A+60-60 = 180-60
A = 120

Now that we know the three angles A = 120, B = 35, C = 25, we can find the missing sides 'b' and 'c'

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We will use the law of sines to find side b
sin(A)/a = sin(B)/b
sin(120)/68 = sin(35)/b
b*sin(120) = 68*sin(35) <<--- cross multiply
b = 68*sin(35)/sin(120)
b = 45.037013350222 <<--- use a calculator; this value is approximate
b = 45.0 <<--- round to the nearest tenth

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Do the same for side c
sin(A)/a = sin(C)/c
sin(120)/68 = sin(25)/c
c*sin(120) = 68*sin(25) <<--- cross multiply
c = 68*sin(25)/sin(120)
c = 33.1838323365404 <<--- use a calculator; this value is approximate
c = 33.2 <<--- round to the nearest tenth