Question

In the Δ ABC shown below, ∠X : ∠Y = 1:2.

Answer 1

Answer:

$\frac{1}{\sqrt{3} }$

Step-by-step explanation:

∠B = 90°

So ∠X + ∠Y + ∠B = 180° (angle sum property of triangles)

∴ ∠X + ∠Y = 90°

Let the common measure of angles be z

∴ 1z + 2z = 90°  (ratio 1:2)

∴ 3z = 90°

∴ z = $\frac{90}{3}$ = 30°

∴ X = 1z = 30° and Y = 2z = 60°

∴ tan x = tan 30°

tan 30° =  $\frac{1}{\sqrt{3} }$

Answer 2

Answer:

ley ∠x = 1z

∠y =2z

∠B =90

∠x+ ∠y + ∠B =180

∠x+ ∠y=180-90

∠x + ∠y=90

1z+2z=90

3z =90

z =90/3

z =30

x=1z

=1(30)

=30

y=2z

=2(30)

=60

tan x =tan 30

tan 30 =1/√3