Question

In triangleXYZ, angleXYZ = 90°, angle YZX=30° and angle YXZ=60° seg XY = 4cm then find seg XZ.
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Answer 1

Answer:

In the figure (given in the attachment),

In triangle XYZ is a right triangle with ∠Y= 90° , ∠YXZ=60° , ∠YZX = 30° and XY=4 cm.

Since , \tan \theta=\dfrac{perpendicular}{base}tanθ=

base

perpendicular

So , \sin Z=\dfrac{XY}{XZ}sinZ=

XZ

XY

\begin{gathered}\Rightarrow\sin30^{\circ}=\dfrac{4}{XZ}\\\\\Rightarrow\ \dfrac{1}{2}=\dfrac{4}{XZ}\\\\\Rightarrow\ XZ=4\times2=8\end{gathered}

⇒sin30

∘

=

XZ

4

⇒

2

1

=

XZ

4

⇒ XZ=4×2=8