Question

determine the length of x, to the nearest tenth of a kilometre.
a) 2400.0 km
b) 2100.0 km
c) 990.9 km
d) 1737.5 km

Explanation:

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

In the right - triangle with the \(39^{\circ}\) angle and hypotenuse \(2400\) km, the adjacent side \(a\) (let's call it) can be found using the cosine function: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(a = 2400\times\cos39^{\circ}\approx2400\times0.7771\approx1865.04\) km.

Step2: Find the length of \(x\)

In the right - triangle with the \(49^{\circ}\) angle and adjacent side \(a\approx1865.04\) km (from Step 1), we use the tangent function \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(x=a\times\tan49^{\circ}\). Substitute \(a = 1865.04\) km, then \(x=1865.04\times\tan49^{\circ}\approx1865.04\times1.1504\approx1737.5\) km.

Answer:

d) \(1737.5\) km