Question

what is the missing length of this problem? ​

Answer 1

Answer is

$x = 9$

$y = \frac{9 \sqrt{2} }{2}$

Step-by-step explanation:

Since there are two given angles 45 and 90 we can use the triangle interior angle theorem to find the missing angle

$45 + 90 + x = 180$

$135 + x = 180$

$x = 45$

The missing angle is 45

This is a 45 45 90 triangle. This means they are two side length that are equal. The legs or the side that make the 90 degree angle are equal in length. So the given side length and y are the legs.

Since the given side length is

$\frac{9 \sqrt{2} }{2}$

y is also

$\frac{9 \sqrt{2} }{2}$

to find x we can apply the pythagorean theorem to find x

$a {}^{2} + {y}^{2} = {x}^{2}$

where a and y are the legs and x is the hypotenuse

Plug it in

$( \frac{9 \sqrt{2} }{2} ) {}^{2} + (\frac{9 \sqrt{ {2} } }{2} ) {}^{2} = {x}^{2}$

$\frac{81}{2} + \frac{81}{2} = {x}^{2}$

${x}^{2} = \frac{162}{2}$

$162 \div 2 = 81$

$x {}^{2} = 81$

$x = 9$