In the same circle, chord ab determines a 115° arc and chord ac determines a 43° arc. find m∠bac.

36° or 101°

Step-by-step explanation:

Consider the figures given in the attachment.

Point C can be between A and B as shown in the left image of the attachment or outside AB chord as shown in the right image.

In both figures, ∠AOB = 115° and ∠AOC = 43°.

Both the triangles are isoceles triangle as OC and OA side is equal in ΔAOC and OA and OB is equal in ΔAOB.

In ΔAOC,

∠A + ∠O + ∠C = 180°

∠A = ∠C

∴ 2 ∠A =180-43=137°

∴∠A = 68.5

In ΔAOB,

∠A + ∠B + ∠O = 180°

∠A = ∠B

∴2 ∠A = 180-115=65°

∴∠A = 32.5°

For figure on the left side,

∠BAC = ∠OAC - ∠OAB = 68.5 - 32.5 =36°

For figure on right side,

∠BAC = ∠OAC + ∠OAB = 68.5 + 32.5 =101°

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step-by-step explanation:

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680