A sandbox in a playground has side lengths of 23 feet, 35 feet, and 40 feet. What are the measures of the angles between the sides?

Question

A sandbox in a playground has side lengths of 23 feet, 35 feet, and 40 feet. What are the measures of

the angles between the sides?

Answer 1

To solve an SSS triangle:

1. use The Law of Cosines first to calculate one of the angles.
2. then use The Law of Cosines again to find another angle.
3. and finally use angles of a triangle add to 180° to find the last angle.

Acute scalene triangle.

Sides: a = 23 b = 35 c = 40

Area: T = 400.654

Perimeter: p = 98

Semiperimeter: s = 49

Angle ∠ A = α = 34.915° = 34°54'55″ = 0.609 rad

Angle ∠ B = β = 60.574° = 60°34'25″ = 1.057 rad

Angle ∠ C = γ = 84.511° = 84°30'40″ = 1.475 rad

Height: h_a = 34.84

Height: h_b = 22.895

Height: h_c = 20.033

Median: m_a = 35.781

Median: m_b = 27.536

Median: m_c = 21.84

Inradius: r = 8.177

Circumradius: R = 20.092

Vertex coordinates: A[40; 0] B[0; 0] C[11.3; 20.033]

Centroid: CG[17.1; 6.678]

Coordinates of the circumscribed circle: U[20; 1.922]

Coordinates of the inscribed circle: I[14; 8.177]

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

∠ A' = α' = 145.085° = 145°5'5″ = 0.609 rad

∠ B' = β' = 119.426° = 119°25'35″ = 1.057 rad

∠ C' = γ' = 95.489° = 95°29'20″ = 1.475 rad