Solving for Bearings

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Question 1 of 7

Find the bearing of

$C$ from

$A$

$AC=$ (124) $°T$

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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.

Notice that when starting from North and heading to East, the two lines form a complementary angle.

Since complementary angles add up to

$90°$ , we find the value of

$theta$ and add it to

$90°$ to get the true bearing of

$C$ from

$A$ .

To solve for

$theta$ , we can use the known values that are opposite and adjacent to it.

Since we have the opposite and adjacent values, we can solve for

$tan theta$

$tan theta$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}$

$tan theta$	$=$	$\frac{\color{#004ec4}{4}}{\color{#00880A}{6}}$

$tan theta$	$=$	$0.6666…$

Remember that we are looking for

$theta$ , not

$tan theta$

Use your calculator to find the value of

$theta$ . The common key combinations on your calculator would be:

$\text(Shift) +tan+0.6666…$

$or$

$tan^(-1)+0.6666…$

This will give you the value of

$33.69°$ or

$33°41’$ , depending on the calculator.

Next, round the value to the nearest degree. For rounding values:

Degrees with decimals:

Decimal value below 50: Round down

Decimal value 50 or above: Round up

Degrees with minutes:

Minute value below 30: Round down

Minute value 30 or above: Round up

This will give us

$theta=34°$ .

Finally, add

$34°$ to

$90°$ to find the true bearing of

$C$ from

$A$ .

$AC$	$=$	$90+34$
	$=$	$124°T$

$AC=124°T$

Question 2 of 7

2. Question
Bianca leaves her home and cycles due north for $12km$ , then $7km$ due west to the gym. What is the bearing of her home from the gym?
- $HG=$ (150) $°T$
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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.

Notice that when starting from North and heading to East, the two lines form a complementary angle.

Since complementary angles add up to $90°$ , we find the value of $theta$ and add it to $90°$ to get the true bearing of $H$ from $G$ .

To solve for $theta$ , we can use the known values that are opposite and adjacent to it.

Since we have the opposite and adjacent values, we can solve for $tan theta$

$tan theta$ $=$ $\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}$

$tan theta$ $=$ $\frac{\color{#004ec4}{12}}{\color{#00880A}{7}}$

Remember that we are looking for $theta$ , not $tan theta$

Use your calculator to find the value of $theta$ . The common key combinations on your calculator would be:

$\text(Shift) +tan+(12/7)$ $or$ $tan^(-1)+(12/7)$

This will give you the value of $59.74°$ or $59°45’$ , depending on the calculator.

Next, round the value to the nearest degree. For rounding values:

Degrees with decimals:

Decimal value below 50: Round down

Decimal value 50 or above: Round up

Degrees with minutes:

Minute value below 30: Round down

Minute value 30 or above: Round up

This will give us $theta=60°$ .

Finally, add $60°$ to $90°$ to find the true bearing of $H$ from $G$ .

$HG$ $=$ $90+60$

$=$ $150°T$

$HG=150°T$

Question 3 of 7

Town

$A$ is

$128 \text(km)$ east and

$165 \text(km)$ south of town

$B$ . Find the true bearing of town

$A$ from town

$B$ .

Round your answer to the nearest minute

$BA=$ (142) $°$ (12) $'T$

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