Question

question 11 (1 point) which trigonometric tool must be used to determine the length of x in the diagram shown? a) the sine law b) primary trigonometric ratios c) the pythagorean theorem d) two of the above are required

Explanation:

Step1: Analyze the triangle

We have a right - angled triangle (with a right angle) where we need to find the length of a side.

Step2: Recall trigonometric tools

• The sine law is used for non - right - angled triangles (\(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)).
• Primary trigonometric ratios (\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}},\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)) are used for right - angled triangles.
• 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.

In this case, we have a right - angled triangle. First, we can use the Pythagorean theorem to find the base of the larger right - angled triangle (let's call it \(y\)): \(y=\sqrt{74^{2}-55^{2}}\). Then, for the smaller right - angled triangle with angle \(47^{\circ}\), we can use the primary trigonometric ratio \(\sin47^{\circ}=\frac{x}{y}\) (after finding \(y\) from the Pythagorean theorem)

Answer:

d) two of the above are required