Question

d) 1.5 cm 19.5 cm x

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use trigonometric ratios. The side opposite to angle \(x\) is \(1.5\) cm and the hypotenuse is \(19.5\) cm. The sine of an angle in a right - triangle is defined as \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin(x)=\frac{1.5}{19.5}\)

Step2: Simplify the fraction

Simplify \(\frac{1.5}{19.5}\). We can multiply both the numerator and the denominator by 10 to get rid of the decimals: \(\frac{1.5\times10}{19.5\times10}=\frac{15}{195}\). Then divide both by 15: \(\frac{15\div15}{195\div15}=\frac{1}{13}\approx0.0769\)

Step3: Find the angle \(x\)

To find \(x\), we take the inverse sine (arcsin) of \(0.0769\). So, \(x = \arcsin(0.0769)\)
Using a calculator, \(\arcsin(0.0769)\approx4.41^{\circ}\) (rounded to two decimal places)

Answer:

\(x\approx4.41^{\circ}\) (or if we want to keep it more precise, we can use the exact fraction \(\arcsin(\frac{1}{13})\))