Question

question 9 (mandatory) (1 point)
which trigonometric tools must be used to determine the length of x in the diagram
shown?
a) the sine and tangent ratios
b) the sine law and the tangent ratio
c) the sine and cosine laws
d) the cosine law and the tangent ratio

Explanation:

Step1: Analyze the triangles

We have two right - angled triangles. For the left - hand triangle with angle \(65^{\circ}\), we can use the sine ratio (\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)) to find the length of the common side (let's call it \(y\)). Then for the right - hand triangle with angle \(27^{\circ}\), we can use the tangent ratio (\(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\)).
First, for the triangle with angle \(65^{\circ}\) and hypotenuse \(225\) m. Using the sine ratio: \(\sin65^{\circ}=\frac{y}{225}\), so \(y = 225\times\sin65^{\circ}\).

Step2: Use the result in the second triangle

For the triangle with angle \(27^{\circ}\), we know the opposite side \(y\) (from step 1) and we want to find the adjacent side \(x\). Using the tangent ratio: \(\tan27^{\circ}=\frac{y}{x}\), so \(x=\frac{y}{\tan27^{\circ}}\). Substituting \(y = 225\times\sin65^{\circ}\) into the second equation, we use both sine and tangent ratios.

Answer:

a) the sine and tangent ratios