Homework Help

[Helpame]

:?: Can you please help me on the following 4 Problems (If you know how to do it can you show your work):

1) Lance bikes 6 miles due north, then 5 miles due east and lastly, 3 miles due north again. To the nearest tenth of a mile, how far, in a straight line distance, is Lance from his starting point?

2)In triangle DEF, angle D is 1 more than twice angle E and angle F is 7 less than angle d. What is the number of degrees in the angle of the triangle with the greatest measure?

3) A sea captain at location A observes the measure of the angle of elevation to the top of a cliff to be 18 degrees. This measure changes 28 degrees when his ship is at location B. If the height of the cliff is known to be 760 feet, how far has the ship moved from location A to location B?

Note: there were no pictures with any of them.

Please help.

 

[stapel]

1) How far north, in total, does he go? How far east?

Draw the right triangle. Use the Pythagorean Theorem to find the length of the hypotenuse. Round to one decimal place.

2) Assuming "D" and "d" to be, contrary to common usage, the same thing, pick a variable for the measure of angle E. Write an expression, in terms of this variable, for "one more than twice" this value, being an expression of the measure of angle D. In terms of this expression, construct a new expression meaning "seven less than" the measure of angle D.

Recall the angle-sum value for any triangle. Add the variable and the two expressions. Set equal to this angle sum. Solve for the variable. Back-solve for the other two angle measures. List, as your answer, whichever of the three values is largest.

3) Does the exercise say "changes 28°", so the new angle of elevation is 18° + 28° = 46°? Or does the exercise say (as is more common, but not at all required) "changes to 28°"?

In either case, draw the first right triangle, with the height being the known value of 760 and the base being the distance across the water. The hypotenuse is the line of sight, and the angle given is the one down on the water at the ship.

Label the angle with "18°"; don't label the base yet..

Draw the second triangle, nested inside the first. (If the angle is larger, whether 28° or 46°, then the triangle is smaller.) The height is the same, and the base is "x".

Go back to the first triangle. Label the little bit of base that isn't shared with the second triangle as "y", so the total length of the big (original) triangle is x + y.

Now use trig ratios to solve for the values of x and y (or at least of y, since this indicates the change in location).

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[Helpame]

Oh, thank you so much, that really helped me.

 

[stapel]

Glad I could help!

By the way, regarding your note about the lack of pictures: Very often a large part of solving these sorts of exercises lies in drawing a good picture. Don't be afraid to grab some scratch paper and see what you can come up with. You'd be surprised how often just roughing out the word problem on paper can similify the whole process.

Eliz.