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# Trigonometry Word Problems

## Applications of trigonometric ratios.

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Measuring Mountains

How do we measure the world’s highest mountains? Explorers measured the height of Mount Everest a century before Sir Edmund Hillary reached the top. They used right triangles to find the mountain’s height.

#### Triangles and Tangents

In the 1850s, British mapmakers decided to measure India and Nepal. They wanted to determine accurate heights for the mountains. To measure Mount Everest, they picked a spot 160 miles from the base of the mountain and used surveying tools to sight the peak. They measured the angle to the top of the mountain. Since they had an angle and an adjacent side of an imaginary triangle, they could figure out the height of the opposite side using the tangent function, which gave them the altitude of the mountain.

Using trigonometry, the British geographers calculated the altitude of Mount Everest to be 29,002 feet. In 1999, scientists used a GPS transmitter to measure the height of the peak and found that the altitude was actually 29,035 feet. That means that the measurement of the first geographers was only 33 feet off!

Even though thousands of people climb Mount Everest each year, it remains a dangerous challenge. See for yourself: http://www.youtube.com/watch?v=bcnQPDtOkyM

#### Explore More

People who climb Mount Everest can’t do it alone. The Sherpa people, an ethnic group from the Himalayas, are an essential part of every climb. They act as guides for the climbers and save many lives each year. While tourists see the mountain as a once-in-a-lifetime climb, the Sherpas climb it constantly. Watch the videos below to learn more about the lives of the Sherpas of Everest.

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