Question

1 find the missing side length.
a) 10.36 b) 9.66
c) 7.19 d) 6.94

Explanation:

Step1: Use trigonometric ratio (tangent)

In a right - angled triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 46^{\circ}\), the adjacent side is \(x\) and the opposite side is \(10\). But wait, no! Wait, using the sine rule for a right - angled triangle. Wait, no, for a right - angled triangle with angle \(\theta = 46^{\circ}\), we know that \(\sin46^{\circ}=\frac{\text{opposite}}{\text{hypotenuse}}\) is not relevant. Wait, using \(\tan46^{\circ}=\frac{10}{x}\) (since \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\) in a right - angled triangle where the side of length \(10\) is opposite to the \(46^{\circ}\) angle and \(x\) is adjacent to the \(46^{\circ}\) angle)
\(\tan46^{\circ}\approx1.0355\)
So, \(1.0355=\frac{10}{x}\)

Step2: Solve for \(x\)

Cross - multiply: \(x=\frac{10}{1.0355}\approx9.66\)

Answer:

b) \(9.66\)