Question

What is the value of x?

x=___

Answer 1

x = 4

Explanation:

I noticed right away that triangle JLM is a 45-45-90 triangle. If we can find the length of JL, we can find x easily.

sin 30° = (opposite side) / (hypotenuse), or

(opposite side) = (hypotenuse)(sin 30°)

= 8√2(1/2) = 4√2

Thus, side JL has length 4√2. This is also the length of the hypotenuse of triangle JLM. Here, the length of x (length of LM) is found using the sine function:

sin 45° = x / (4√2), which can be rewritten as

x = (4√2)(sin 45°) =

1

4√2· ------- = 4

√2

Thus, x = 4

Answer 2

x = 4

Explanation:

Look at the picture.

ΔKJL is a triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.

Therefore if KL = 8√2, then JL = KL : 2 = 8√2 : 2 = 4√2.

ΔLJM if a triangle 45° - 45° - 90°. The sides are in ratio 1 : 1 : √2.

Therefore if JL = 4√2, then LM = 4√2 : √2 = 4