Question

in triangle xyz,angle y=90°,angle z= a°,angle x =(a+30)°,xz=24,then find xy and yz​

Answer 1

Answer:

xy = 12

yz = 12√3

Step-by-step explanation:

Sum of angles in triangle = 180°

=> a + ( a + 30 ) + 90 = 180

=> 2a + 120 = 180

=> 2a = 60

=> a = 30

So ∠z = 30° and ∠x = 60°.

Method 1 (trigonometry)

cos ∠x = xy / xz

=>  xy = xz cos ∠x = 24 cos 60° = 24 × (1/2) = 12

cos ∠z = yz / xz

=> yz = xz cos ∠z = 24 cos 30° = 24 × √3 / 2 = 12√3

Method 2 (Pythagoras)

Since ∠x = 60°, triangle xyz is half of an equilateral triangle

=> xy = half of one side of the equilateral triangle

=> xy = (1/2) × xz = (1/2) × 24 = 12

By Pythagoras' Theorem,

yz = √(xz² - xy²) = √(24² - 12²) = 12√(2² - 1²) = 12√(4 - 1) = 12√3

Answer 2

using basic trigonometry.


I hope you will get it.