Question

Find x. 0 48.0 0 64.2 0 41.9 O 25.8

Answer 1

x = 25.8° (option D)

Step-by-step explanation:

We need to find the third side before we can find the angle x.

Triangle is right-angled

Using pythagoras theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = 30,

opposite = side oposite the angle x = ?

adjacent = 27

30² = opposite² + 27²

900 = opposite² + 729

opposite² = 900 - 729

opposite² = 171

opposite = √171 = 13.08

We can now apply sine ratio:

`\begin{gathered} \frac{a}{\sin\text{ A}}=\text{ }\frac{c}{\sin \text{ C}} \\ \text{The small square represent angle 90 degre}es \end{gathered}`
`\begin{gathered} \frac{30}{\sin\text{ 90}}=\frac{13.08}{si\text{ n x}} \\ \sin \text{ x (30) = 13.08 (sin 90)} \end{gathered}`
`\begin{gathered} 30(\sin \text{ x) = 13.08} \\ \sin \text{ x = }(13.08)/(30) \\ \sin \text{ x = }0.436 \\ x=sin^(-1)0.436 \\ x\text{ = 25.85}\degree \end{gathered}`

x = 25.8° (option D)