Question

Help ? i need to find the missing side length in special right triangles

Answer 1

Use Cosine to find 'n'.


`\sf~Cosine=(Adjacent)/(Hypotenuse)`

Plug in what we know:


`\sf~cos(45^o)=(n)/(6√(2))`

Simplify the cosine of 45 degrees and 6 times the square root of 2:


`\sf~0.707106781=(n)/(8.48528137)`

Multiply 8.48528137 to both sides:


`\sf~n=6`

Now that we have 'n', we can use the Pythagorean Theorem to find 'm'.


`\sf~a^2+b^2=c^2`

Where 'a' and 'b' are the two legs of the right triangle and 'c' is the hypotenuse.

Plug in what we know:


`\sf~a^2+6^2=(6\sqrt2)^2`

Simplify the exponents:


`\sf~a^2+36=72`

Subtract 36 to both sides:


`\sf~a^2=36`

Find the square root of both sides:


`\sf~a=√(36)`


`\sf~a=6`

So 'n' and 'm' are both equal to 6.