Question

question 1 (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 cosine law
c) the sine law
d) the pythagorean theorem

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 cosine law (\(c^{2}=a^{2}+b^{2}-2ab\cos C\)) is used in non - right - angled triangles when we know two sides and the included angle or all three sides.
• The sine law (\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)) is used in non - right - angled triangles when we know an angle and its opposite side and another side or angle.
• The Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\)) is used in right - angled triangles to relate the sides.

Step2: Analyze the given diagram

We have two right - angled triangles (since there are right angles in the diagram). For each right - angled triangle, if we consider the angles (\(39^{\circ}\) and \(49^{\circ}\)) and the side of length \(2400\) km, we can use the primary trigonometric ratios. For example, if we consider one of the right - angled triangles, say the one with angle \(39^{\circ}\) and hypotenuse \(2400\) km, and we want to find the height \(x\) (opposite side to the angle), we use \(\sin\theta=\frac{opposite}{hypotenuse}\), i.e., \(\sin39^{\circ}=\frac{x}{2400}\). Similarly, for the other right - angled triangle with angle \(49^{\circ}\), we can also use primary trigonometric ratios.

Answer:

A. primary trigonometric ratios