Question

Triangle lmn is right angled at m. If m angle n=45°,whst is the length of mn in cm,if nl=9√2cm?

Answer 1

Answer:

9 cm

Step-by-step explanation:

∠m = 90°  ( right angled at m)

∠n = 45°

∠l + ∠m + ∠ n = 180°

=> ∠l + 90° + 45° = 180°

=> ∠l = 45°

This is an isosceles right angles triangle

lm = mn = a cm

ln = 9√2 cm

applying Pythagoras theorem

ln² =lm² + mn²

=> (9√2)² = a² + a²

=> 81 * 2 = 2a²

=> a² = 81

=> a = 9

length of mn = 9 cm