Question

question 6 (mandatory) (1 point)
determine the length of x, to the nearest tenth of a kilometre.
39° 2400 km 49°
x
a) 2100.0 km
b) 990.9 km
c) 1737.5 km
d) 2400.0 km

Explanation:

Step1: Find the length of the common side (let's call it \( h \)) in the left - hand right - triangle

Using the sine function in the left - hand right - triangle with angle \( 39^{\circ} \) and hypotenuse \( 2400\) km.
The formula for sine is \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( h = 2400\times\sin(39^{\circ}) \).
Since \( \sin(39^{\circ})\approx0.6293 \), then \( h = 2400\times0.6293=1510.32\) km.

Step2: Find the length of \( x \) in the right - hand right - triangle

Using the tangent function in the right - hand right - triangle with angle \( 49^{\circ} \) and opposite side \( x \) and adjacent side \( h \).
The formula for tangent is \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). So, \( x = h\times\tan(49^{\circ}) \).
Since \( \tan(49^{\circ})\approx1.1504 \) and \( h = 1510.32\) km, then \( x=1510.32\times1.1504\approx1737.5\) km.

Answer:

C. \( 1737.5\) km