Superlesson
Project 10-1

Superlesson
Project 10-2

Superlesson
Project 10-3

Advanced Algebra

Chapter 10, Trigonometry

For surveyors, the ability to measure distances accurately is a practical matter. For vulcanologists--scientists who study volcanoes--it can be a matter of life and death.

Part A, Law of Cosines

1. Use the Volcanic Deformation Project Web site to answer the following questions.

a. What use do vulcanologists in the Volcano Deformation Project make of EDM (electronic distance measurement)?

b. The volcano Mount St. Helens in the state of Washington erupted in 1980. View the slide show of the eruption at this Web site. Suppose that on May 17, 1980, a vulcanologist used EDM to measure the distance to the nearest point on the bulge described in Slide #3. How much more quickly would a laser pulse make the round trip from the EDM instrument to the point on the bulge and back again than it would have before the bulge began to appear? (A laser beam travels at the speed of light, 186,282.3976 mi/sec.) Express your answer in scientific notation.

c. View the lava dome in Slide #23. Find lengths AC and BC (ft). (Assume that the width given as "nearly" is exact.)


d. Find .

e. A vulcanologist at A made EDM measurements of a lava dome as shown. Use the Law of Cosines to find BD. Then find the height of the dome.

Part C, Making Connections

2.View the before and after photos of Mount St. Helens taken from nearby Spirit Lake at this Web site.

a. What are the elevations of the volcano before and after the eruption?

b. From the top of the "old" Mount St. Helens, the angle of depression of the spot at Spirit Lake where the photos were taken was 16.41°. From the top of the "new" mountain, the angle is 13.95°. Use the Law of Sines and the difference in elevations between the old and new mountains to find length SB (ft).

c. Find BC, the height of Mount St. Helens above Spirit Lake today.

d. Find the elevation of Spirit Lake above sea level.