Question

If m∠A = 72°, m∠B = 32°, and c = 8, what are the measures of the remaining sides and angle? (2 points)

A. m∠C = 76°, a = 3.59, b = 7.79

B. m∠C = 76°, a = 4.37, b =7.84

C. m∠C = 76°, a = 7.84, b = 4.37

D. m∠C = 76°, a = 7.79, b = 3.59

Answer 1

To find the measures of the remaining sides and angle, we can use the Law of Sines. Using the Law of Sines, we can calculate the lengths of sides a and b. Then, using the angle sum of a triangle, we can find angle C.

Step-by-step explanation:

To find the measures of the remaining sides and angle, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In this case, we can use the law to find the lengths of sides a and b, and then use the angle sum of a triangle to find angle C.

Using the Law of Sines:

a/sin(A) = c/sin(C)

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

Plugging in the values:

a/sin(72°) = 8/sin(C)

b/sin(32°) = 8/sin(C)

Solving for a and b, we get:

a ≈ 3.59

b ≈ 7.79

Now, we can find angle C using the angle sum of a triangle:

m∠C = 180° - m∠A - m∠B

m∠C ≈ 180° - 72° - 32°

m∠C ≈ 76°

Therefore, the measures of the remaining sides and angle are:

m∠C ≈ 76°, a ≈ 3.59, b ≈ 7.79

Answer 2

D

Sides: a = 7.841 b = 4.369 c = 8

Step-by-step explanation:

Symbols definition of ABC triangle

You have entered side c, angle α, and angle β.

Acute scalene triangle.

Sides: a = 7.841 b = 4.369 c = 8

Area: T = 16.621

Perimeter: p = 20.211

Semiperimeter: s = 10.105

Angle ∠ A = α = 72° = 1.257 rad

Angle ∠ B = β = 32° = 0.559 rad

Angle ∠ C = γ = 76° = 1.326 rad

Height: ha = 4.239

Height: hb = 7.608

Height: hc = 4.155

Median: ma = 5.116

Median: mb = 7.614

Median: mc = 4.928

Inradius: r = 1.645

Circumradius: R = 4.122

Vertex coordinates: A[8; 0] B[0; 0] C[6.65; 4.155]

Centroid: CG[4.883; 1.385]

Coordinates of the circumscribed circle: U[4; 0.997]

Coordinates of the inscribed circle: I[5.736; 1.645]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 108° = 1.257 rad

∠ B' = β' = 148° = 0.559 rad

∠ C' = γ' = 104° = 1.326 rad