Question

11 - cloc > non - right angled trigonometry > applications for the cosine law > q2 > question 2 a plane flying from vancouver to edmonton, a distance of 830 km. a navigational error was discovered and it was determined the plane had flown 17° off course from the beginning of the flight for 450 km. how far was the plane from edmonton when the error was discovered? answer rounded to 1 decimal place. > show answer

Explanation:

Step1: Identify the sides and angle for cosine - law

Let the distance from Vancouver to Edmonton be $c = 830$ km, the distance the plane has flown be $a = 450$ km, the unknown distance from the plane to Edmonton be $b$, and the angle between the intended path and the actual - flown path $\theta=17^{\circ}$. The cosine - law formula is $b^{2}=a^{2}+c^{2}-2ac\cos\theta$.

Step2: Substitute the values into the cosine - law formula

Substitute $a = 450$, $c = 830$, and $\theta = 17^{\circ}$ into the formula. First, calculate $\cos(17^{\circ})\approx0.9563$. Then, $a^{2}=450^{2}=202500$, $c^{2}=830^{2}=688900$, and $2ac\cos\theta=2\times450\times830\times0.9563 = 2\times450\times830\times0.9563=709947$.

Step3: Calculate $b^{2}$

$b^{2}=202500 + 688900-709947=181453$.

Step4: Calculate $b$

$b=\sqrt{181453}\approx426.0$ km.

Answer:

$426.0$ km