a triangular pyramid is formed from three right triangles as shown below. use the information given in the…
a triangular pyramid is formed from three right triangles as shown below. use the information given in the figure to find the length bd. if applicable, round your answer to the nearest whole number. the lengths on the figure are not drawn accurately.
Answer
Explanation:
Step1: Apply Pythagorean theorem in right - triangle BDC
In right - triangle (BDC), by the Pythagorean theorem (BC^{2}=BD^{2}+DC^{2}). In right - triangle (ADC), (AC = 45), (AD = 27), we first find (DC) using the Pythagorean theorem in (\triangle ADC). In (\triangle ADC), (DC=\sqrt{AC^{2}-AD^{2}}). Substitute (AC = 45) and (AD = 27) into the formula: [DC=\sqrt{45^{2}-27^{2}}=\sqrt{(45 + 27)(45 - 27)}=\sqrt{72\times18}=\sqrt{1296}=36]
Step2: Apply Pythagorean theorem in right - triangle BDC again
In right - triangle (BDC), we know (BC = 85) and (DC = 36). Let (BD=x). By the Pythagorean theorem (x=\sqrt{BC^{2}-DC^{2}}). Substitute (BC = 85) and (DC = 36) into the formula: [BD=\sqrt{85^{2}-36^{2}}=\sqrt{(85 + 36)(85 - 36)}=\sqrt{121\times49}=\sqrt{121}\times\sqrt{49}=77]
Answer:
77