Question

explain why trigonometric ratios could not be used to calculate the side marked x in each of the following triangles.
a)
a.
b)
b.
c)
c.

Explanation:

Step1: Recall trig - ratio requirements

Trigonometric ratios (sine, cosine, tangent) are used in right - angled triangles and require the knowledge of an angle and a side length in relation to the unknown side.

Step2: Analyze triangle a

In triangle a, the side \(x\) is not part of a right - angled triangle where we know an acute angle and a side related to \(x\). We have a non - right triangle with an angle and a right - angled part, but \(x\) is not in a position to use trig ratios directly as we don't have the right combination of side and angle in a right - angled sub - structure related to \(x\).

Step3: Analyze triangle b

In triangle b, although we have an angle (\(57^{\circ}\)) and a side length (\(5.8\) cm), the triangle is not a right - angled triangle. Trigonometric ratios are defined for right - angled triangles, so we cannot use them to find \(x\).

Step4: Analyze triangle c

In triangle c, we have a right - angled triangle, but we only know one side length (\(46\) m) and no non - right angle measure that is related to the side \(x\). Without an acute angle measure along with a side related to \(x\), we cannot use trigonometric ratios.

Answer:

In triangle a, \(x\) is not in a right - angled sub - structure suitable for trig ratios. In triangle b, the triangle is not right - angled. In triangle c, no non - right angle related to \(x\) is given.