Question

question 12 (mandatory) (1 point)
which trigonometric tools must be used to determine the length of x in the diagram
shown?
a) the cosine law and the tangent ratio
b) the sine law and the tangent ratio
c) the sine and tangent ratios
d) the sine and cosine laws

Explanation:

Step1: Analyze the triangle structure

The problem involves non - right triangles (where the cosine law is applicable for side - angle - side or side - side - side relationships) and right - triangle parts (where tangent ratios can be used for opposite/adjacent side relationships in right - angled sub - triangles).

Step2: Recall trigonometric tools

The cosine law formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\) (for non - right triangles to find side lengths when two sides and the included angle are known or all three sides are known). The tangent ratio is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) (for right - angled triangles to relate angles and sides).

Answer:

A. the cosine law and the tangent ratio