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KiRa [710]
3 years ago
15

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

Mathematics
1 answer:
miskamm [114]3 years ago
3 0

Answer:

66.4°

Step-by-step 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:

\frac{sin(Z)}{XY}=\frac{sin(X)}{YZ}\\\\Substituting:\\\\\frac{sin(Z)}{6} =\frac{sin(90)}{15}   \\\\sin(Z)=\frac{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°

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