Question

4 find the missing side length.
11
42°
x
a) 14.6
b) 8.17
c) 16.44
d) 12.21

Explanation:

Step1: Use the cosine law

For a right - angled triangle, we can also use the cosine law. The cosine law formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In a right - angled triangle with one non - right angle \(\theta = 42^{\circ}\), adjacent side \(a = 11\), and the hypotenuse \(x\). We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So \(x=\frac{11}{\cos42^{\circ}}\).

Step2: Calculate the value of \(\cos42^{\circ}\)

We know that \(\cos42^{\circ}\approx0.7431\). Then \(x = \frac{11}{0.7431}\approx14.8\)

Answer:

a) \(14.8\)