Question

Find the missing lengths of the sides.

Answer 1

Answer: option a

Explanation:

You can use these identities:

`sin\alpha=(opposite)/(hypotenuse)\\\\cos\alpha=(adjacent)/(hypotenuse)`

Then, to find "a" you know that:

`\alpha=45\°\\adjacent=a\\hypotenuse=9√(2)`

Substituting:

`cos(45\°)=(a)/(9√(2))`

Now you must solve for "a":

`a=cos(45\°)(9√(2))\\\\a=9in`

To find "b", you know that:

`\alpha=45\°\\opposite=b\\hypotenuse=9√(2)`

Substituting:

`sin(45\°)=(b)/(9√(2))`

Now you must solve for "b":

`b=sin(45\°)(9√(2))\\\\b=9in`

Answer 2

The correct answer is A.

EXPLANATION

The given triangle is a right isosceles triangle because one angle is 90° and the base angles will be 45° each.

This means that:

`a = b`

Using, the Pythagorean Theorem, we have

`{a}^(2) + {a}^(2) = {(9 √(2) )}^(2)`

We simplify to get:

`2{a}^(2) = 81 * 2`

`{a}^(2) = 81`

Take positive square root,

`a = √(81)`

This implies that

`a = 9`

Therefore b is also equal to 9

The correct answer is A.