Answer:
x = B. 18 ROOT 2/ROOT 3
Explanation:
There are two Triangles in the diagram above.
Step 1
We would solve for Triangle A First
Using Trigonometric function Cosine
cos θ = adjacent /hypotenuse
θ = 30°
Adjacent = 9 units
Hypotenuse = unknown
cos 30= 9/ Hypothenuse
Cross Multiply
cos 30 × Hypotenuse = 9
Hypotenuse = 9 / cos 30
cos 30 in surd form = √3/2
Hypotenuse = 9/√3/2
Hypotenuse = 9 × 2/√3
= 18/√3 units
Step 2
We would solve for the upper triangle = Triangle B
We are looking for x
θ = 45°
For Triangle B, the Hypotenuse we solved for in Triangle A is equivalent to the adjacent in Triangle B
Therefore ,
Hypotenuse for Triangle A = Adjacent side for Triangle B
θ = 45°
Adjacent = 18/√3 units
Hypotenuse = x = unknown
We would solve for this using Trigonometric function cosine
cos 45 = 18/√3 units / Hypothenuse
Cross Multiply
cos 45 × Hypotenuse = 18/√3 units
Hypotenuse = 18/√3 units / cos 45
cos 45 in surd form = 1/√2
Subtituting, we have
Hypotenuse (x) = 18/√3 units / 1/√2
Hypotenuse (x) = 18/√3 units ×√2/1
= 18× √2/ √3 units
= 18 √2/√3 units
Therefore x = Option B. 18 ROOT 2/ROOT 3