Question

It is given that ΔABC ~ ΔDEF, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then DE = ______ and ∠F = ______.

Answer 1

ΔABC ~ ΔDEF (Given)

∴ ∠C = ∠F (If two triangles are similar, then their corresponding angles are equal)

⇒ ∠F = 50° (∠C = 50°)

Also,

$\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{\mathrm{AC}}{\mathrm{DF}}$ (If two triangles are similar, then their corresponding sides are proportional)

$$\begin{gathered} \Rightarrow \frac{5\mathrm{cm}}{\mathrm{DE}}=\frac{8\mathrm{cm}}{7.5\mathrm{cm}} \\ \Rightarrow \mathrm{DE}=\frac{5\times 7.5}{8}=4.7\mathrm{cm}\left(\mathrm{Approx}\right) \end{gathered}$$

It is given that ΔABC ~ ΔDEF, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then DE = __4.7 cm __ and ∠F = ___50°___.