contestada

1. A boat drifted 15 m out into the water off Ocean Beach, where the shore drops off

at 4°. Can Brooke walk out to bring the boat back without getting water over the

tops of her hip boots which are 1 m tall? Explain your reasoning.


2. are the engineer who designed a new branch for the Mountain Railroad

Company. You sent your plans calling for 100 km of track up Bixby Mountain

taking trains 99 km east of the city of Bixby, to the City Council for approval.

But before the Council got around to looking at your plans, they passed a

regulation that no railroad tracks could go up their mountain at an angle of more

than 8°. Will your plans be approved? Why or why not?


3. The residents of Quietville, a little town 9 km from the San Francisco Airport,

insist that any plane flying over their town disturbs them if it is lower than 3 km.

Will a plane that took off at a 21° angle disturb them? Why?


4. You are an air pollution inspector, checking that factories in your city have

chimneys at least 65 m tall. Standing 50 m from the Ore Smelting Company’s

chimney, you find the angle from the ground to the chimney top is 51°. Can the

company use that chimney legally? Explain.


6. River City is offering a $3 million contract to build a bridge between points A and

C on opposite sides of City River. Along the side of the river that makes a right

angle with the line of the bridge at point C, a surveyor walked 72 m to point B

where she measured the 55° angle form B to A. Long Company will build the

bridge for $3 million if it is not more than 103 m from point A to point C. Short

Company agrees to build it if it is no more the 100 m. Which contracting firm

will be awarded the contract? Why?


7. An elderly woman is trapped 17 m up in her burning home. Can a fireman reach

her on his 26 m ladder if it has to make a 43° angle in order to clear the woman’s

greenhouse under her window? Explain your reasoning.


8. A ski lift 1000 m long goes at a 29° angle up Mt. Gentleslope. Does the lift take

skiers all of the way up to the top of the mountain where there is a snack bar at

the 500 m elevation? Explain your reasoning.


9. Mr. Johnson is a jet pilot who just moved with his family to Suburbia, 26 km

from Toledo Airport. His seven-year-old son, Eric, would like to see his father’s

plane as it flies over their new home for the first time today, but there is a layer of

clouds 5 km above the house. Will Eric be able to see his Dad’s plane if it takes

off at a 9° angle? Explain.


10.You are the cost control expert for an engineering firm designing a giant

television tower having several metal braces, each built in 21 m from the base at a

73° angle with the ground. Part of your job is to decide which standard length of

metal brace wastes less metal: the brace that comes 71 m long, or the one that is

73 m long. What is your decision?

Respuesta :

The correct responses found using trigonometric ratios are as follows;

  1. Brooke's cannot bring the boat back without getting water over her boots.
  2. The plan will not be approved
  3. The plane will not disturb
  4. The company can not use the chimney legally
  6. The Long company will build the bridge
  7. The fireman can reach her.
  8. The lift does not take the skiers up to the bar.
  9. Eric will be able to see his Dad's plane.
  10. The 73 m. brace

How can trigonometric ratios be used to find the right responses?

1. The depth of the water = 15 × tan(4°) = 1.049 m

The height of Brooke's boot = 1 m

Therefore;

  • Brooke's cannot bring the boat back without getting water over her boots.

2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°

Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;

  • The plan will not be approved.

3. Height reached by the plane = 9 × tan(21°) = 3.455

Therefore;

  • The plane will not disturb.

4. Height of the chimney at the factory = 50 × tan(51°) = 61.745

The minimum chimney height = 65 m.

Therefore;

  • The company can not use the chimney legally.

6. Length of the bridge = 72 × tan(55°) ≈ 102.83

Therefore;

  • The Long company will build the bridge because it is longer than 100 m. but not more than 103 m.

7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7

Therefore;

  • The fireman can reach her.

8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8

Therefore;

  • The lift does not take the skiers up to the bar.

9. Height reached by plane = 26 × tan(9°) ≈ 4.12

The plane flies under the cloud therefore;

  • Eric will be able to see his Dad's plane.

10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83

Therefore;

  • The brace that wastes less metal is the 73 m. brace, because the 71 m. brace is not long enough and two braces will be required.

Learn more about trigonometric ratios here:

https://brainly.com/question/24349828

#SPJ1

Otras preguntas