Question

A pilot flies in a straight path for 1 hour and 30 min

Answer 1

Step-by-step explanation

Given that;

The speed of the pilot = 670 miles per hour

The first path took her 1 hour 30 minutes

The second path took her 2 hours

Included angle = 170 degrees

To find the distance from the starting position, follow the steps below

Step 1; Find the distance of the first and second path

Recall, that

`\text{ Distance }=\text{ speed }*\text{ time}`

For the first leg

time = 1 hour 30 minutes

speed = 670 miles per hour

`\begin{gathered} \text{ Distance }=\text{ 1.5}*\text{ 670} \\ \text{ Distance }=\text{ 1005 miles} \end{gathered}`

The first leg = 1005 miles

Second leg

time = 2 hours

speed = 670 miles per hour

`\begin{gathered} \text{ Distance }=\text{ 2 }*\text{ 670} \\ \text{ Distance }=\text{ 1340 miles} \end{gathered}`

The second leg = 1340 miles

apply the cosine rule to find the distance from the starting position

`\text{ a}^2\text{ }=\text{ b}^2\text{ }+\text{ c}^2\text{ - 2bc cos A}`

substitute the given data into the cosine formula

`\begin{gathered} \text{ a}^2\text{ }=\text{ \lparen1005\rparen}^2+\text{ \lparen1340\rparen}^2\text{ - 2\lparen1005}*\text{ 1340\rparen cos 170} \\ \text{ a}^2=\text{ 1010025 }+\text{ 1795600 - 2693400 }*(-0.9848) \\ \text{ a}^2\text{ }=\text{ 2805625 }+2652460.32 \\ \text{ a}^2\text{ }=\text{ 5458085.32} \\ \text{ take the square roots of both sides} \\ √(a^2)\text{ }=\text{ }√(5458085.32) \\ \text{ a }=\text{ 2336.3 miles} \end{gathered}`

Therefore, distance from the starting position is 2336.3 miles