Trotting the Globe

Worksheet Description

This worksheet is a collection of geometry word problems with a theme of global travel and exploration. It presents students with various scenarios involving distances and angles related to traveling, such as the altitude of a plane and its distance to a point on the ground, road trip calculations, and the angles between locations. The problems incorporate real-world applications, like calculating the average speed of a trip, the horizontal distance of a hiker up a mountain, and the curvature of a track.

The aim of the worksheet is to enhance students’ geometric reasoning skills in the context of practical situations that involve traveling. It teaches them to apply mathematical concepts to solve problems on distance, angle measurement, and speed calculations. This worksheet also helps students understand the relevance of geometry in activities like flying, driving, and hiking. By working through these problems, students learn to apply formulas and geometric principles to navigate and understand the world around them.

Example Problems

1. A passenger plane is flying at an altitude of 35,000 feet. If the plane is directly above a point on the ground, what is the distance between the plane and the point on the ground, assuming a straight-line path?

2. A road trip starts at a point A and ends at a point B. If the road trip covers a distance of 400 miles and takes 6 hours to complete, what is the average speed of the journey in miles per hour?

3. Two cars are driving on parallel roads. Car A is 5 miles north of Car B, and the distance between them is 8 miles. Calculate the angle between the two cars, as seen from a bird’s-eye view.

4. A train travels a straight path from Town X to Town Y, a distance of 120 miles. If the train takes 2 hours to complete the journey, what is its average speed in miles per hour?

5. A cruise ship is sailing on the ocean and follows a course that forms a 45-degree angle with the shoreline. If the ship is 3 miles from the shoreline, how far has it traveled along the shoreline?

6. A traveler is hiking up a mountain with a slope of 30 degrees. If the vertical height gained is 1000 feet, calculate the horizontal distance the traveler has covered.

7. A family is taking a road trip, and their route includes a right turn. If they drive 100 miles south and then make a 90-degree right turn, how far west will they travel?