Question

question 16 (mandatory) (1 point)
which trigonometric tool must be used to determine the length of x in the diagram shown?

a) the sine law
b) primary trigonometric ratios
c) the pythagorean theorem
d) two of the above are required

Explanation:

Step1: Analyze the triangle

We have a right - angled triangle (due to the right - angle symbol). To find the length of \(x\), we first need to find some other sides or angles.

Step2: Use the Pythagorean theorem

Let's assume the triangle with sides \(55\) and \(74\). First, find the hypotenuse \(h\) of the non - \(x\) right - angled triangle. By the Pythagorean theorem \(h=\sqrt{55^{2}+74^{2}}=\sqrt{3025 + 5476}=\sqrt{8501}\). But we also have another right - angled triangle with angle \(47^{\circ}\).

Step3: Use primary trigonometric ratios

If we consider the right - angled triangle with angle \(47^{\circ}\), we can use the primary trigonometric ratios. Let's assume the hypotenuse (from the previous step) is related to \(x\). But actually, we can also note that we need to use the Pythagorean theorem (to relate the sides of the right - angled triangles) and primary trigonometric ratios (to relate the sides and angles of the right - angled triangle with the \(47^{\circ}\) angle)

Answer:

d) two of the above are required