Answer:
4.6cm
Step-by-step explanation:
A diagram showing the analysis from the question has been attached to this response. Kindly download it and view.
From the diagram,
=> We have three angles given
(i) the right angle, 90°
(ii) the angle opposite to side x, 50°
(iii) the angle opposite to side y, 40°
=> We also have one side given,
(i) the hypotenuse, of length 6cm
We can therefore apply the sine rule as follows;
[tex]\frac{sin 90^0}{6} = \frac{sin 50^0}{x} = \frac{sin 40^0}{y}[/tex] ---------------(i)
Now to get the value of x, we'll equation the first and second terms of equation (i) as follows;
[tex]\frac{sin 90^0}{6} = \frac{sin 50^0}{x}[/tex] [cross multiply]
[tex]xsin90^0 = 6 sin 50^0[/tex]
[tex]x * 1 = 6 * 0.7660[/tex]
[tex]x =4.596[/tex] cm = 4.6cm [to the nearest tenth]
Therefore, the value of x is 4.6cm to the nearest tenth
