Question

question 5 (mandatory) (1 point)
which trigonometric tool must be used to determine the length of x in the diagram shown?

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

Explanation:

• The sine law is used when we have a relationship between angles and sides in non - right - angled triangles. Here, we have two right - angled triangles formed by the altitude \(x\).
• The cosine law is used when we know two sides and the included angle or all three sides of a non - right - angled triangle.
• The Pythagorean theorem is used in right - angled triangles when we know two sides and want to find the third. But here we don't know two sides of a single right - angled triangle to directly apply it.
• Primary trigonometric ratios (\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}},\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)) can be used. If we consider the two right - angled triangles:
• Let's assume the two right - angled triangles. For one triangle with angle \(39^{\circ}\) and hypotenuse \(2400\) km, \(x\) is the opposite side. Using \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), we have \(x = 2400\times\sin39^{\circ}\). For the other triangle with angle \(49^{\circ}\), we could also use a similar trigonometric ratio approach.

Answer:

c) primary trigonometric ratios