Question

In ΔXYZ, ∠X=45° and ∠Y=61°. ∠XWZ=90° and XY=24. Find the length of XW to the nearest integer.

Answer 1

15

Explanation:

<XZY = 180-45-61 = 74°

according to sines rule :

XZ/sin Y = XY/sin Z

XZ/sin 61 = 24/sin 74

=> XZ = 24×sin 61 / sin 74

= 24× 0.87/ 0.96

= 21.75

XW/XZ = sin 45

=> XW = XZ × sin 45

= 21.75 × 0.71

= 15.44 = 15