Answer:
[tex]\frac{12}{25}[/tex] ↔ sinD × cosD
[tex]\frac{3}{5}[/tex] ↔ sinC
[tex]\frac{16}{15}[/tex] ↔ cosC × tanD
[tex]\frac{4}{5}[/tex] ↔ sinD
Step-by-step explanation:
In the given triangle CBD
∵ ∠B is a right angle
∴ CD is the hypotenuse
→ We can use the trigonometry ratios
∵ sinC = opposite side of ∠C ÷ hypotenuse
∴ sinC = [tex]\frac{BD}{DC}[/tex]
∵ BD = 3 and CD = 5
∴ sinC = [tex]\frac{3}{5}[/tex]
∵ cosC = adjacent side of ∠C ÷ hypotenuse
∴ cosC = [tex]\frac{BC}{DC}[/tex]
∵ BC = 4 and CD = 5
∴ cosC = [tex]\frac{4}{5}[/tex]
∵ tanC = opposite side of ∠C ÷ adjacent side of ∠C
∴ tanC = [tex]\frac{BD}{BC}[/tex]
∵ BD = 3 and BC = 4
∴ tanC = [tex]\frac{3}{4}[/tex]
∵ sinD = opposite side of ∠D ÷ hypotenuse
∴ sinD = [tex]\frac{BC}{DC}[/tex]
∵ BC = 4 and CD = 5
∴ sinD = [tex]\frac{4}{5}[/tex]
∵ cosD = adjacent side of ∠D ÷ hypotenuse
∴ cosD = [tex]\frac{BD}{DC}[/tex]
∵ BD = 3 and CD = 5
∴ cosD = [tex]\frac{3}{5}[/tex]
∵ tanD = opposite side of ∠D ÷ adjacent side of ∠D
∴ tanD = [tex]\frac{BC}{BD}[/tex]
∵ BD = 3 and BC = 4
∴ tanD = [tex]\frac{4}{3}[/tex]
Let us find the answer to each tile
→ sinD = [tex]\frac{4}{5}[/tex] ⇒ 4th answer
→ sinC = [tex]\frac{3}{5}[/tex] ⇒ 2nd answer
→ sinD × cosD = ( [tex]\frac{4}{5}[/tex]) × ([tex]\frac{3}{5}[/tex]) = [tex]\frac{12}{25}[/tex] ⇒ 1st answer
→ tanC × tanD = [tex]\frac{3}{4}[/tex] × [tex]\frac{4}{3}[/tex] = 1 ⇒ Not used
→ cosC × tanD = [tex]\frac{4}{5}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{15}[/tex] ⇒ 3rd answer
