Question

As the figure shows, Jack wants to drive to Point C from Point A. He has to drive 15 km to point B first. Then he turns 65 degrees and drives another 10 km. How far is the distance from point A to point C?Round your answer to two decimal points.

Answer 1

the distance from point A to point C is 21.26 km

Step-by-step explanation:

We need to find the distance from point A to point C. To get this, we need to know the angle facing AC

65° + ∠CBA = 180° (sum of angles on a line)

∠CBA = 180 - 65

∠CBA = 115°

To solve for the distance, let's make an illustration of the information we have:

Now we can use cosine rule to find the distance AC:

`\begin{gathered} co\sin e\text{ rule :} \\ b^2=a^2+c^2\text{ -2acCosB} \\ a\text{ = side opposite }\angle\text{A = 10km} \\ b\text{ = side opposite }\angle B\text{ = AC} \\ c\text{ = side opposite }\angle C\text{ = 15 km} \\ \angle B\text{ = 115}\degree \end{gathered}`

substitute the values into the formula:

`\begin{gathered} AC^2=10^2+15^2\text{ - 2(10)(15)}*\cos \text{ 115}\degree \\ AC^2\text{ = 100 + 225 - 300(-0.4226)} \\ AC^2\text{ = 325 + }126.78 \\ AC^2\text{ = 45}1.78 \\ AC\text{ = }\sqrt[]{\text{ 45}1.78} \\ AC\text{ = }21.2551 \end{gathered}`

To two decimal point, the distance from point A to point C is 21.26 km