Using Bearings to Find Distance 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
Question 1 of 4
1. Question
Find the distance the speedboat has traveled due south `(AB)`
Round your answer to two decimal places- (164.54) `\text(km due South)`
Hint
Help VideoCorrect
Well Done!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$A true bearing is an angle measured clockwise from the True North around to the required direction.First, find the value of angle `CAB`.Notice that angle `CAB` is part of the given bearing, which also consists of a straight angle from the North line clockwise to the South line.
To find the value of angle `CAB`, simply subtract the measure of the straight angle, `180°`, from the given bearing.`/_CAB` `=` `210°-180°` `=` `30°` To solve for line `AB`, we can use the known values of the hypotenuse and angle `CAB`.
Use `cos` to find the value of line `AB`.`cos` `30°` `=` $$\frac{\color{#00880A}{AB}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos` `30°` `=` $$\frac{\color{#00880A}{AB}}{\color{#e85e00}{\text{190}}}$$ `cos30°``xx190` `=` `((AB)/190)``xx190` Multiply both sides by `190` `190cos30°` `=` `AB` Using your calculator, `190cos30°=164.54`.Therefore, the speedboat is `164.54 \text(km)` due South.
`164.54 \text(km due South)` -
Question 2 of 4
2. Question
Find the distance (`d`) the boat has traveled from the port (`P`)
Round your answer to the nearest kilometre- `d=` (25) `\text(km)`
Hint
Help VideoCorrect
Excellent!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$A true bearing is an angle measured clockwise from the True North around to the required direction.To solve for line `d`, we can use the known values of the line adjacent to the bearing.
Use `cos` to find the value of line `d`.`cos48°` `=` $$\frac{\color{#00880A}{\text{adjacent}}}{\color{#e85e00}{d}}$$ `cos48°` `=` $$\frac{\color{#00880A}{17}}{\color{#e85e00}{d}}$$ `cos48°``xxd` `=` `((17)/d)``xxd` Multiply both sides by `d` `dcos48°` `=` `17` `dcos48°``divcos48°` `=` `17``divcos48°` Divide both sides by `cos48°` `d` `=` `17/(cos48°)` Divide both sides by `cos48°` Using your calculator, `17/(cos48°)=25.46`.Rounding it to the nearest kilometre, the boat traveled `25 \text(km)` from the port.
`25 \text(km)` -
Question 3 of 4
3. Question
A ship has traveled `72 \text(km)` North West from the port (`O`). How far North (`y_n`) of the starting point has it traveled?
Round your answer to one decimal place- `y_n=` (50.9) `\text(km)`
Hint
Help VideoCorrect
Keep Going!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$A true bearing is an angle measured clockwise from the True North around to the required direction.To solve for the line `y_n`, we can use the known values of the hypotenuse and the given angle `(45°)`.Remember `NW` (North West) means `45°`.
Use `cos` to find the value of line `y_n`.`cos45°` `=` $$\frac{\color{#00880A}{{y_{n}}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos45°` `=` $$\frac{\color{#00880A}{{y_{n}}}}{\color{#e85e00}{72}}$$ `cos45°``xx72` `=` `((y_n)/72)``xx72` Multiply both sides by `72` `72cos45°` `=` `y_n` `y_n` `=` `72cos45°` Using your calculator, `72cos45°=50.9`.Therefore, the boat traveled `50.9 \text(km)` to the North.
`y_n=50.9 \text(km)` -
Question 4 of 4
4. Question
A ship has traveled `51 \text(km)` from the port (`P`) with a bearing of `N 67°E`. How far east (`x_e`) has it traveled?
Round your answer to one decimal place- `x_e=` (46.9) `\text(km)`
Hint
Help VideoCorrect
Great Work!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$A true bearing is an angle measured clockwise from the True North around to the required direction.To solve for `x_e`, we can use the known values of the hypotenuse and the given angle, `(67°)`.
Use `sin` to find the value of line `x_e`.`sin67°` `=` $$\frac{\color{#004ec4}{x_e}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin67°` `=` $$\frac{\color{#004ec4}{x_e}}{\color{#e85e00}{51}}$$ `sin67°``xx51` `=` `((x_e)/51)``xx51` Multiply both sides by `51` `51sin67°` `=` `x_e` `x_e` `=` `51sin67°` Using your calculator, `51sin67°=46.9`.Therefore, the boat traveled `46.9 \text(km)` to the East.
`x_e=46.9 \text(km)`