Answer:
x ≈ 37.53
Step-by-step explanation:
To find the value of x, we will follow the steps below:
first, we need to find angle z
z+47° +90° = 180° (sum of interior angle of a triangle)
z + 137° = 180°
subtract 137° from both-side of the equation
Z + 137°-137° = 180° - 137°
Z=43°
angle Z = 43°
We can now use the sine rule to find the value of x
Using the sine rule
[tex]\frac{sin Z}{z} = \frac{sin X}{x}[/tex]
where Z and X are angles and z and x are side length
from the diagram given,
X = 47° and we find Z to be 43°
side z = 35
we can now proceed to substitute the values into the formula
[tex]\frac{sin 43}{35}[/tex] = [tex]\frac{sin 47}{x}[/tex]
cross-multiply
x sin 43° = 35 sin 47°
divide both-side of the equation by sin 43°
x sin 43° /sin 43°= 35 sin 47° /sin 43°
x ≈ 37.53 to two decimal place
