Question

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

Explanation:

Step1: Analyze the triangle with \(225m\) side

First, use the Law of Sines in the non - right triangle. The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let's assume the triangle with sides and angles where we can find a side (let's call it \(y\)) adjacent to the right - triangle part.

Step2: Use the tangent ratio

After finding the side \(y\) (using the Law of Sines), in the right - triangle part (where \(x\) is a side), we use the tangent ratio. The tangent ratio is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). If we know an angle (say \(\alpha\)) in the right - triangle and the side \(y\) (adjacent or opposite depending on the angle), we can find \(x\).

Answer:

A. the sine law and the tangent ratio