Answer: X = 13.2 (Approximated to the nearest tenth)
Step-by-step explanation: This is a right angled triangle, with one side given, and one angle given. We can calculate the other two sides provided the reference angles are known, and in this question, all angles are known. One is 90°, the second is 47° while the third is 43° (that is 180° - {90° + 47°} )
We shall use angle 47 as the reference angle, and note that the line that lies between the reference angle and the right angle is the adjacent. Note also that the unknown side is the hypotenuse, (the side facing the right angle).
Now that we have established two sides of the triangle, the adjacent (9 units) and the hypotenuse (X), we can calculate the unknown side by using the trigonometrical ratio of cosine.
Cos 47 = adjacent/hypotenuse
Cos 47 = 9/X
By cross multiplication we now have
X/1 = 9/Cos 47
By checking your table of values or by use of your calculator, cos 47 is equal to 0.6819
Therefore
X = 9/0.6819
X = 13.19 units
However, by rounding up to the nearest tenth,
X = 13.2 units
