Question

find x. round all values to the nearest tenth to calculate the next value. round your final answer to the tenth as well.

Explanation:

Step1: Find the height (h) of the left triangle

In the left right - triangle, we know the hypotenuse \( c = 33 \) and the angle \( \theta=24^{\circ} \). We use the sine function, where \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \). The opposite side to the angle \( 24^{\circ} \) is the height \( h \) of the triangle. So \( \sin(24^{\circ})=\frac{h}{33} \), then \( h = 33\times\sin(24^{\circ}) \).
Calculating \( \sin(24^{\circ})\approx0.4067 \), so \( h=33\times0.4067\approx13.4211 \).

Step2: Find \( x \) using the right - triangle on the right

In the right - triangle on the right, we know the angle \( \alpha = 40^{\circ} \) and the opposite side to this angle is \( h\approx13.4211 \). We use the tangent function, where \( \tan\alpha=\frac{\text{opposite}}{\text{adjacent}} \). Here, the adjacent side to the angle \( 40^{\circ} \) is \( x \), and the opposite side is \( h \). So \( \tan(40^{\circ})=\frac{h}{x} \), which can be rewritten as \( x=\frac{h}{\tan(40^{\circ})} \).
We know that \( \tan(40^{\circ})\approx0.8391 \) and \( h\approx13.4211 \). Then \( x = \frac{13.4211}{0.8391}\approx16.0 \) (rounded to the nearest tenth).

Answer:

\( 16.0 \)