Question

Find the measure of the missing sides in each special right triangle. Simplest radical form

Answer 1

Answer:

X=$8\sqrt{2}$                   Y=$7\sqrt{2}$

Step-by-step explanation:

The first one is 45-45-90 right angled isosceles triangle.

The length of the hypotenuse ie.X can be found with the help of Pythagoras Theorem.

$a^{2} + b^{2} = X^{2}$

where a and b are the remaining sides of the triangle,

$8^{2} +8^{2} =X^{2} \\2*8^{2} =X^{2}\\X=8\sqrt{2}$

X=$8\sqrt{2}$  

In the second triangle we have to apply trigonometry,

cos θ=$\frac{Length OfAdjacentSide}{LengthOfHypotenuse}$

cos 30°=$\frac{\sqrt{3} }{2}$

$\frac{\sqrt{3} }{2}$=$\frac{Y}{14}$

Thus, Y=$7\sqrt{2}$  inches