Answer:
∠TAC is approximately equal to 61.6°
Step-by-step explanation:
The given parameters for the pyramid are;
The dimension for the rectangular base are; Length = 9 cm, width = 7 cm
The length of the diagonal sides, TA, TB, TC, and TD = 12 cm each
The midpoint of the rectangular base = Point M
The diagonal AC = AM + MC
AM = MC as given M is the midpoint of the rectangular base
∴ AC = AM + MC = 2·AM
By Pythagoras' theorem, AC = √(9² + 7²) = √130
AC = √130 cm
∴ AM = AC/2 = (√130)/2 cm
Alternatively, AM = √((9/2 cm)² + (7/2 cm)²) = √(32.5) cm
∠TAC = ∠TAM
By trigonometric ratios, we have;
