Question

In ∆ XYZ, ∠X = 90⁰, ∠Y = 60⁰. If XZ = 5√3 cm, what is the length of seg YZ and XY?

Answer 1

Step-by-step explanation:

plz mark it as brainliest

Answer 2

Given:

∆ XYZ

∠X = 90⁰, ∠Y = 60⁰

XZ = 5√3 cm

Find YZ=XY=?

In triangle XYZ,

∠X+∠Y+∠Z=180°  

90° + 60° + ∠Z = 180°

150° + ∠Z = 180$Cos30\°=\frac{YZ}{XZ}$

∠Z = 180° - 150°

∠Z =30°

NOW

$Sin30\°=\frac{XY}{XZ}$

$\frac{1}{2} =\frac{XY}{5\sqrt{3} }$

$XY=\frac{5\sqrt{3} }{2}$

$\frac{\sqrt{3} }{2}=\frac{YZ}{5\sqrt{3} }$

$YZ=\frac{5\sqrt{3} \sqrt{3} }{2}$

$YZ=\frac{5\times 3}{2}$

$YZ=\frac{15}{2}$

Hence the value of XY =5√3/2 and YZ=15/2