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 (\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}},\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)) are used in right - angled triangles.
• The cosine law (\(c^{2}=a^{2}+b^{2}-2ab\cos C\)) is used for 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 for 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 for right - angled triangles to relate the sides.

Step2: Analyze the given diagram

We have two right - angled triangles (the small right - angled triangle with side \(x\) and the larger right - angled triangle with side \(2400\) km). For the right - angled triangle where we can find \(x\), if we consider one of the right - angled triangles (say the one with the \(39^{\circ}\) angle or \(49^{\circ}\) angle), we can use the primary trigonometric ratios. For example, if we take the right - angled triangle with the \(39^{\circ}\) angle and hypotenuse \(2400\) km, and \(x\) as the opposite side to the \(39^{\circ}\) angle, we can use \(\sin39^{\circ}=\frac{x}{2400}\) (or if we consider the other right - angled triangle with the \(49^{\circ}\) angle, we can also use primary trigonometric ratios).

Answer:

a) primary trigonometric ratios