Question

1. solve for x. round to the nearest tenth.

x =

Explanation:

Step1: Find the angle inside the triangle

Use the sine function. $\sin\theta=\frac{opposite}{hypotenuse}$. Let the angle inside the triangle be $\theta$. $\sin\theta=\frac{43}{45}$.
$$\theta=\sin^{- 1}(\frac{43}{45})\approx73.4^{\circ}$$

Step2: Find \(x\)

Since \(x\) and \(\theta\) are supplementary (\(x+\theta = 180^{\circ}\) as they form a linear - pair).
$$x = 180^{\circ}-\theta$$
Substitute \(\theta\approx73.4^{\circ}\) into the equation.
$$x=180 - 73.4=106.6^{\circ}$$

Answer:

\(106.6\)