Question

question 14 (mandatory) (1 point)
which trigonometric tool must be used to determine the length of x in the diagram shown?

a) primary trigonometric ratios
b) the sine law
c) the pythagorean theorem
d) the cosine law

Explanation:

Step1: Recall trigonometric tools

Primary trigonometric ratios (\(\sin\theta=\frac{opposite}{hypotenuse},\cos\theta = \frac{adjacent}{hypotenuse},\tan\theta=\frac{opposite}{adjacent}\)) are used in right - angled triangles. The sine law (\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)) is used in non - right - angled triangles. The Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\)) is used to relate the sides of a right - angled triangle (no angles involved in the formula). The cosine law (\(c^{2}=a^{2}+b^{2}-2ab\cos C\)) is used in non - right - angled triangles.

Step2: Analyze the given diagram

The diagram has two right - angled triangles. For each right - angled triangle, if we know an angle and a side, we can use the primary trigonometric ratios. For example, if we consider one of the right - angled triangles with angle \(39^{\circ}\) or \(49^{\circ}\) and the side \(2400\) km, we can use \(\tan\theta=\frac{x}{...}\) (where \(x\) is the opposite side in one of the right - angled triangles) or other primary trigonometric ratios depending on the sides and angles relationship in the right - angled sub - triangles.

Answer:

a) primary trigonometric ratios