Answer:
The distance between the two cars is approximately 237 meters.
Step-by-step explanation:
Let be P the top of the high-rise building and Q and R the location of the two cars from each side of the tower. Geometric figure is represented on image attached below. We calculate the distance between both cars ([tex]d[/tex]), measured in meters, by Trigonometric ratios:
[tex]d = QO + OR[/tex]
[tex]d = \frac{OP}{\tan 45^{\circ}} +\frac{OP}{\tan 60^{\circ}}[/tex]
Where [tex]OP[/tex] is the height of the building, measured in meters.
[tex]d = OP\cdot \left(\frac{1}{\tan 45^{\circ} }+\frac{1}{\tan 60^{\circ}} \right)[/tex]
If we know that [tex]OP = 150\,m[/tex], then:
[tex]d = (150\,m)\cdot \left(\frac{1}{\tan 45^{\circ}}+\frac{1}{\tan 60^{\circ}} \right)[/tex]
[tex]d \approx 236.603\,m[/tex]
The distance between the two cars is approximately 237 meters.
