Question

List the angles of the triangle in order from least to greatest. OPTIONS : ∠C,∠B,∠A, ∠B,∠A,∠C, ∠A,∠B,∠C , ∠C,∠A,∠B

Answer 1

Answer:

∠B,∠A,∠C

Step-by-step explanation:

∠B is between the two longest sides so it would be the smallest angle.

∠C is between the two shortest sides so it would be the largest angle.

this leaves ∠A to be in between them.

∠B,∠A,∠C

OR

cosine rule:

∠A = cos -¹ ( [8.8² + 5.1² - 6.8²] / 2[8.8][5.1] )

∠A = 50.404 (5 sig. fig.)

∠B = cos -¹ ( [8.8² + 6.8² - 5.1²] / 2[8.8][6.8] )

∠B = 35.304 (5 sig. fig.)

∠C = cos -¹ ( [6.8² + 5.1² - 8.8²] / 2[6.8][5.1] )

∠C = 94.291 (5 sig. fig.)

∠B,∠A,∠C

Answer 2

The angles of the triangle listing in order from the least to greatest is ∠B, ∠A and ∠C.

Sum of angle in a triangle

The sum of angles in a triangle is 180 degrees. Therefore,

∠A + ∠B + ∠C = 180°

Therefore, let's find ∠A using cosine rule

a = 6.8

b = 5.1

c = 8.8

a² =  b²+ c² - 2bc cos A

a² - b² - c² = - 2bc cos A

cos A = a² - b² - c² / -2bc

cos A = 6.8² - 5.1² - 8.8² / - 2 × 5.1 × 8.8

cos A = 46.24 - 26.01 - 77.44 / -89.76

cos A = -57.21 / -89.76

cos A = 0.63736631016

A = cos⁻¹ 0.63736631016

A = 50.4043120147

∠A = 50.40°

b² =  a²+ c² - 2ac cos B

cos B = b²- a²- c² / - 2ac

cos B = 5.1² - 6.8² - 8.8² / - 2 × 6.8 × 8.8

cos B = 26.01 - 46.24 - 77.44 / -119.68

cos B = -97.67 / -119.68

cos B = 0.81609291443

B = cos⁻¹ 0.81609291443

∠B = 35.3044294443

∠B = 35.30°

Therefore,

∠C = 180 - 50.40 - 35.30 = 94.30°

Therefore, the angles of the triangle listing in order from the least to the greatest is ∠B, ∠A and ∠C.

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