Question

Solve for x and y in the given the 45° - 45° - 90° triangle shown above. When applicable, simplify all radicals and show your work.

Answer 1

Answer:

Therefore,

$x=y= 4\sqrt{2}=5.6568\ units$

Step-by-step explanation:

Given:

Consider In Right Angle Triangle ABC

∠B = 90°

∠C = ∠A = 45°

AB = y

BC = x = adjacent side

AC = 8 = hypotenuse

To Find:

x = ?

y = ?

Solution:

In Right Angle Triangle ABC by Cosine Identity we have

$\cos C = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}$

substituting the above given values we get

$\cos 45 = \dfrac{BC}{AC}=\dfrac{x}{8}$

$\dfrac{1}{\sqrt{2} } =\dfrac{x}{8}\\\therefore x=\dfrac{8}{\sqrt{2} } \\Rationalizing\ we\ get\\\therefore x=\dfrac{8}{\sqrt{2}}\times \dfrac{\sqrt{2} }{\sqrt{2}}}\\\therefore x=4\sqrt{2}=4\times 1.4142=5.6568\ units$

As The triangle is 45 - 45 - 90

It is an Isosceles Right triangle

$x=y$..... Isosceles Triangle property

$\therefore y=4\sqrt{2}=4\times 1.4142=5.6568\ units$

Therefore,

$x=y= 4\sqrt{2}=5.6568\ units$