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Find volume of the pyramid from its side face

AD is the height of the triangular pyramid ABCD that has BC = 1, CD = 2, ∠BCD = 120° and dihedral ∠BC = 45°. Find the volume of the pyramid.

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Find the perimeter of a triangle with a bisector

The bisector of a triangle divides its side into segments of length 28 and 12, and the difference of the other two sides is 18. Find the perimeter of the triangle.

Ref:5

log(a, x) = (2/3)log(a, b) - (1/3)log(a, c)

Solve the equation for x. Simplify the solution.

Ref:4

Find angles of triangle 3, 4, 5

The lengths of the triangle's sides are: 3, 4, 5. Find all the angles.

Ref:1

Find angles of triangle 2, 3, 4

The lengths of the triangle's sides are: 2, 3, 4. Find all the angles.

Ref:2

Find angles of triangle 1, 2, 3

The lengths of the triangle's sides are: 1, 2, 3. Find all the angles.

Ref:3

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