Question

Find x in these 45°-45°-90° triangles.



x =

Answer 1

2sqrt(3) or sqrt(12)

Explanation:

Since both angle are 45, opposite lengths are equal

Using pythagoras theorem:

(sqrt24)² = x² + x²

24 = 2x²

x² = 12

x = sqrt(12)

x = 2sqrt(3)

Answer 2

2 sqrt(3) =x

Explanation:

We know that

cos theta = adjacent side/ hypotenuse

cos 45 = x / sqrt(24)

Multiply each side by sqrt(24)

sqrt(24) cos 45 = x

sqrt(24) * sqrt(2)/2 = x

sqrt(48)/2 =x

sqrt(16 *3) /2 =x

sqrt(16) sqrt(3) /2 =x

4 sqrt(3)/2 =x

2 sqrt(3) =x