Mi Lighthouses
mi lighthouses
 |
No items matching your keywords were found.
math help?
could you explain to how to do this as well as the answer.
1. The angle of elevation from a boat to the top of a lighthouse is 35°. The lighthouse is 96 ft tall. How far from the base of the lighthouse is the boat?
a 7 ft
b137 ft
c 167 ft
d 6 ft
2. Ming launched a model rocket from 20 m away. The rocket traveled straight up. Ming saw it peak at an angle of 70°. If she is 1.5 m tall, how high did the rocket fly?
a 55 m
b 2 m
c 20 m
d 57 m
3. An airplane is flying 2.5 mi above the ground. If the pilot must begin a 3° descent to an airport runway at that altitude, how far is the airplane from the beginning of the runway (in ground distance)?
a 48 mi
b 47 mi
c 5 mi
d 8 mi
For these trigonometry questions, remember the following line:
SOH CAH TOA (Suck a Toe?)
This means, in a right angle triangle,
Sin(x) = Opposite / Hypotenuse
Cos(x) = Adjacent / Hypoetenus
Tan(x) = Opposite / Adjacent
So, let's solve these questions.
1. The angle of elevation from a boat to the top of a lighthouse is 35°. The lighthouse is 96 ft tall. How far from the base of the lighthouse is the boat?
When you draw this diagram out, you see instantly that it is a right-angle triangle. This allows us to use the above equations. Since we have the angle (x), as well as the opposite (96), and we need to find the line that is adjacent, the best equation to use in this case would be tan(x).
tan(x) = Opposite / Adjacent
tan(35) = 96 / Adjacent
Adjacent = 96 / tan(35)
Adjacent = 137.142
So, the lighthouse is approximately 137 ft away from the boat. So the answer is b. 137 ft
2. Ming launched a model rocket from 20 m away. The rocket traveled straight up. Ming saw it peak at an angle of 70°. If she is 1.5 m tall, how high did the rocket fly?
So, after drawing out this diagram, we see that Ming is 20m away from the right-angle, and the angle of elevation from where her EYE LEVEL is, is 70°. We need to find out how high the rocket went. So, since we have the angle, as well as the adjacent line, and we need to find the opposite line, the best equation to use would be one again, tan(x).
tan(x) = Opposite / Adjacent
tan(70) = Opposite / 20
Opposite = tan(70) * 20
Opposite = 54.95
But since she is 1.5m tall, we need to add 1.5 to the height, since she "saw" it peak at an angle of 70°. So, the height the rocket flew was 55 + 1.5 = 56.5, which is approximately 57m. So, the answer should be d. 57 m
3. An airplane is flying 2.5 mi above the ground. If the pilot must begin a 3° descent to an airport runway at that altitude, how far is the airplane from the beginning of the runway (in ground distance)?
After drawing out this diagram, we can see that we have the angle of 3° on the OUTSIDE of the right angle triangle. So, we need to find the degrees on the inside. Since the outside of that angle is 3°, then that means the other angle within the right-angle triangle is also 3° (the angle from where the plan will land). We also know the height of 2.5mi of the plane. We need to find the ground distance, or line that is adjacent to the 3°. So, we have the degrees (x), the adjacent, and the opposite(2.5). The best equation to use, once again, would be tan(x).
tan(x) = Opposite / Adjacent
tan(3) = 2.5 / Adjacent
Adjacent = 2.5 / tan(3)
Adjacent = 47.7
So, the airplane is approximately 48 miles from the beginning of the runway in ground distance, so the answer is:
a. 48 mi
 |
Lighthouses of Northwest Michigan (MI) (Images of America) List Price: $19.99 Sale Price: $13.59  |
|
After the first settlers reached northwestern Michigan, the region's immense pine forests were quickly cultivated into a thriving lumber industry. Coastal towns sprang up to support sawmills, and soon lumber schooners arrived to carry large loads of timber to ports across Lake Michigan... |
 |
Lighthouses of Southwest Michigan (MI) (Images of America) List Price: $21.99 Sale Price: $14.29 |
|
As the coastal towns of southwestern Michigan began to grow in the 1800s, commerce and shipping traffic flourished, making way for the development of lighthouses to ensure vessels' safe passage into port... |
 |
Great Lakes Lighthouses Encyclopedia List Price: $35.00 Sale Price: $21.95 |
|
"Very useful for transportation, architecture, local, and comprehensive collections. Highly recommended." -- Choice "If you own only one lighthouse book, this is the one to buy." -- Great Laker This comprehensive, full-color encyclopedia features more than 650 lighthouses located on all five of the Great Lakes. |
 |
Adobe Photoshop Lightroom 3 List Price: $299.99 Sale Price: $139.99 |
|
Adobe Photoshop Lightroom 3 software helps you bring out the best in your photography, whether you're perfecting one image, searching for ten, processing hundreds, or organizing thousands. Create incredible images that move your audience... |
 |
Ladies of the Lights: Michigan Women in the U.S. Lighthouse Service List Price: $22.95 Sale Price: $13.43 |
|
"A great read about some great ladies, Pat Majher's Ladies of the Lights pays long overdue homage to an overlooked part of Great Lakes maritime history in which a select group of stalwart women beat the odds to succeed in a field historically reserved for men... |
 |
Cana Island Lighthouse (WI) (Images of America) List Price: $21.99 Sale Price: $14.81 |
|
The Cana Island Lighthouse is one of the most picturesque of any lighthouses still operating on the Great Lakes today. The beautiful peninsula of Door County has a long and bountiful tradition of maritime history, including its many lighthouses... |
 |
Lighthouses of Michigan: A Guidebook and Keepsake (Lighthouse Series) List Price: $9.95 Sale Price: $5.94 |
|
For lighthouse lovers in the Midwest, here is a charming guide to Michigan's lighthouses--nearly fifty of them--situated on three Great Lakes. It offers not only history and travel information but also a beautiful full-color souvenir of the state... |
 |
Guarding Door County: Lighthouses and Life-Saving Stations (WI) (Images of America) List Price: $21.99 Sale Price: $14.19 |
|
Jutting out of Wisconsin into the blue waters of Lake Michigan, the scenic peninsula of Door County is endowed with the longest coastline of any county in the nation. Since the mid-1800s, the region has boasted a strong maritime industry, dependent on the constant vigilance and efforts of U... |
 |
Eastern Great Lakes Lighthouses, 2nd: Ontario, Erie, and Huron List Price: $19.95 Sale Price: $4.99 |
|
Eastern Great Lakes Lighthouses combines the fascinating history and lore of lighthouses with stunning color and black-and-white photographs. The stories of the most significant lighthouses on Lakes Ontario, Erie, and Huron--on both the American and Canadian sides--come alive in the stirring profiles and photos contained in these pages... |
 |
The Ultimate Guide to West Michigan Lighthouses List Price: $16.95 Sale Price: $16.95 |
|
This is the ultimate guide book for any lighthouse aficionado. It is also the only book currently in print to feature the two new lighthouses built on the east side of Michigan since 1995. This book includes three different types of directions to find each light, a direct route from nearest major intersection, GPS Waypoints, and a scenic route which follows paved roads around the coastline of Michigan with turn by turn directions... |
