Question

7. Find the missing lengths of the sides.

Answer 1

Answer:

$a=9\ in\\b= 9\ in$

Step-by-step explanation:

This straight triangle has two angles equal to 45 ° and two equal sides.

We know that the side opposite the 90 degree angle is:

$c =9\sqrt{2}\ in$

Since the triangle has two equal angles, then it is an iscoceles triangle.

This means that

$a = b$

We use the Pythagorean theorem to find b

$c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9$

Answer 2

Answer:

x = 7, y = 9.9

Step-by-step explanation: