Question

question 3 (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 pythagorean theorem
c) the cosine law
d) primary trigonometric ratios

Explanation:

Step1: Analyze the triangle properties

We have two right - angled triangles. The primary trigonometric ratios (sine, cosine, tangent) relate the sides and angles of a right - angled triangle. For a right - angled triangle with an angle \(\theta\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

Step2: Check other methods

• The Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\)) is used when we know two sides of a right - angled triangle to find the third side, but we don't have two side lengths in the relevant sub - triangle for direct Pythagorean use here.
• The sine law (\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)) is used for non - right - angled triangles.
• The cosine law (\(c^{2}=a^{2}+b^{2}-2ab\cos C\)) is also used for non - right - angled triangles.

Since we have right - angled triangles (the small triangles formed by the perpendicular), the primary trigonometric ratios are applicable.

Answer:

d) primary trigonometric ratios