Question

question 3 (mandatory) (1 point)
determine the length of x, to the nearest tenth of a kilometre.
2400 km
39°
49°

a) 1737.5 km
b) 2400.0 km
c) 2100.0 km
d) 990.9 km

Explanation:

Step1: Find the adjacent side of \(39^{\circ}\)

Let's first find the adjacent side \(y\) of the right - triangle with angle \(39^{\circ}\) and hypotenuse \(2400\) km. Using the cosine function \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(y = 2400\times\cos39^{\circ}\).

$$y=2400\times0.7771459615\approx1865.15$$

Step2: Find \(x\)

Now, consider the right - triangle with angle \(49^{\circ}\), adjacent side \(y\approx1865.15\) km and opposite side \(x\). Using the tangent function \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), so \(x=y\times\tan49^{\circ}\).

$$x = 1865.15\times1.150368407\approx1737.5$$

Answer:

A. \(1737.5\) km