A perfect app or calculator does this easily. (Since you"re asking here, you"re obviously not unwilling to use an innovation to help.)

_____

Given two sides and also the had angle, the legislation of Cosines can help you discover the third side.

You are watching: Solve the triangle. b = 36°, a = 41, c = 20

... B² = a² + c² - 2ac·cos(B)

... B² = 38² + 18² -2·38·18·cos(36°) ≈ 661.26475

... B ≈ 25.715

Then the law of Sines can help you uncover the various other angles. It have the right to work fine to discover the smaller sized angle first (the one the opposite the shortest side). That way, you can tell if the larger angle is obtuse or acute.

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

... C = arcsin(c/b·sin(B)) ≈ 24.29515°

This angle and also angle B add to much less than 90°, so the remaining angle is obtuse. (∠A can also be found as 180° - ∠B - ∠C.)

... A = arcsin(a/b·sin(B)) ≈ 119.70485°

b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°

Step-by-step explanation:

* To resolve a triangle we can use cosine rule and also sin rule

* In ΔABC

- If a, b, c are the lengths the its 3 sides, where

# a is the contrary to edge A

# b is opposite to edge B

# c is the opposite to angle C

- By utilizing the cosine rule:

# a² = b² + c² - 2bc cos(A)

# b² = a²² + c² - 2ac cos(B)

# c² = a² + b² - 2ab cos(C)

- By using sin rule

# c/sinC = a/sinA = b/sinB

* allows solve the problem

∵ a = 42 , c = 18 , m∠B = 36°

* we will usage the cosine rule

∴ b² = (42)² + (18)² - 2(42)(18) cos(36) =864.766 ⇒ take it √ because that both sides

∴ b = 29.4

* currently we will use the sin rule to uncover m∠C

∵ 29.4/sin(36) = 18/sin(C) ⇒ by using cross multiplication

∴ sin(C) = 18 × sin(36°)/29.4 = 0.3598685

∴ m∠C = 21.1°

* The amount of the measure up of the inner angle of a triangle is 180°

∴ m∠A = 180° - (36° + 21.1°) = 122.9°

* b = 29.4 devices , m∠A = 122.9 , m∠C = 21.1°

B=36

a=38

c=18

b=25.7

a-b-c (SSS) {a^2=b^2+c^2-2ab(CosA)

38^2=25.7^2+18^2-2(25.7)(18)(CosA)

1444=660.49+324-925.2(CosA)

1444=984.49-935.2(CosA)

459.51=-935.2(CosA)

-0.491349443969204=CosA

A=119.43

b-B-C (SAA) (SinC)/c=(SinB/b)

(SinC)/18=(Sin36)/25.7

(SinC)/18=0.022871021489979

SinC=0.411678386819631

C=24.31

A=119.43

B=36

C=24.31

a=38

b=25.7

c=18

It is a triangle:

Step-by-step explanation:

b² = a² + c² - 2(a)(c)cos(B)

b² = 41² + 20² - 2(41)(20)cos(36)

b² = 754.2121292

b = 27.46292281

b = 27.463

A = 41, B = 27.4, C = 17

See below

Step-by-step explanation:

When you have actually 2 sides and the angle in between them you usage the cosine organize or legislation of cosines:

After you have a side and the opposed angle (side b and also angle B), you use the legislation of sines:

I will calculate edge A first:

Same for angle C:

The amount of the angles is 36° + 61.2° + 25.3° = 122.5°; The sum have to be 180° therefore this isnt a triangle.

I re go the trouble using B together 63° instead of 36° in situation you composed it wrong and I gained a satisfactory answer.

using B = 36:

b = 36.6

angle A = 86.4°

angle C = 29.1°

A+B+C = 86.4° + 29.1° + 63° = 178.5° ~ 180°

Step-by-step explanation:

i dont also know bruh

That can not be a ideal triangle

Yes this is a Triangle

36 degrees of any side climate 41 would connct come 36 and 17 would connects to 36 and 41! If this is khan Academy her asking out of that a Yes, that is a Triangle

HOPE ns THE BRANLIESS UwU
C = 82.8° b = 27.5 Here"s the working in situation you should see it. Using legislation of Cosines to very first find b: b² = a² + c² - 2acCOS(B) b² = (41)² + (20)² - 2(41)(20)COS(36) b = around 27.5 Now using law of Sines to uncover A sin(36) / (27.5 = sin(A) / (41) sin(A) = 41sin36 / 27.5 sin(A) = 0.876334376145 A = SinInverse(0.876334376145) A = about 61.2° Now utilizing 180-61.2-36 to find B = 82.8° Have a good day!

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