The measure of side length x in the triangle is approximately 15 meters.
The correct option is D) 15 meters.
The figure in the question is a triangle.
To solve for the missing side length, we simply use the cosine rule:
It can be expressed as:
x² = a² + b² - 2ab( cos X )
From the figure:
a = 17 m
b = 22 m
Angle X = 42 degrees
x =?
Plug the given values into the above formula and solve for x:
x² = a² + b² - 2ab( cos X )
x² = 17² + 22² - ( 2 × 17 × 22 × cos(42) )
x² = 289 + 484 - ( 748 × 0.7431 )
x² = 773 - 555.8388
x² = 217.1612
x = √217.1612
x = 14.7
x ≈ 15 meters
Therefore, the side length 'x' measures 15 meters.
Option D) 15 meters is the correct answer.