Question

Find the angle of XYZ give your answer to 1 decimal place

Answer 1

66.4°

Explanation:

To find the angle XYZ, we are to use sine rule. For this, we have to first find ∠Z.

Given that: ∠X = 90° (right angle), XY = 6 cm, YZ = 15 cm. Hence:

`(sin(Z))/(XY)=(sin(X))/(YZ)\\\\Substituting:\\\\(sin(Z))/(6) =(sin(90))/(15) \\\\sin(Z)=(sin(90)*6)/(15)\\\\sin(Z)=0.4\\\\Z=sin^(-1)(0.4)\\\\Z=23.6^o`

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

90 + ∠Y + 23.6 = 180

113.6 + ∠Y = 180

∠Y = 180 - 113.6

∠Y = 66.4°

∠Y = ∠XYZ = 66.4°