Using Bearings to Find Distance 1
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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
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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
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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
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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)`
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