Math / Trigonometry

QuestionIdentifying Trig Ratios (Diagram), Level 1 Score: $4 / 5$ Penalty: 1 off
Question Show
Express $\cos M$ as a fraction in simplest terms.
L But Answer Attempt 1 out of 2 7/23887042/9158711ce9be57d3a43284ce62380145

Studdy Solution

STEP 1

What is this asking? We need to find the cosine of angle $M$ in a right triangle, and write it as a simplified fraction. Watch out! Don't mix up the sides!
Make sure you're using the correct sides for the cosine calculation.

STEP 2

1. Find the hypotenuse.
2. Calculate $\cos M$ .
3. Simplify the fraction.

STEP 3

Alright, so we've got a right triangle, and we know two sides: $LM = 6$ and $LK = 8$ .
We need the hypotenuse, $MK$ , before we can find $\cos M$ .
Let's use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

STEP 4

Plugging in our values, we get $6^2 + 8^2 = MK^2$ .
This simplifies to $36 + 64 = MK^2$ , so $100 = MK^2$ .
Taking the square root of both sides gives us $MK = 10$ .
Remember, the hypotenuse is always positive!

STEP 5

Now, let's remember what cosine means: adjacent over hypotenuse.
Looking at angle $M$ , the adjacent side is $LM = 6$ , and we just found the hypotenuse, $MK = 10$ .

STEP 6

So, $\cos M = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{LM}{MK} = \frac{6}{10}$ .

STEP 7

We can simplify $\frac{6}{10}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .

STEP 8

Dividing $6$ by $2$ gives us $3$ , and dividing $10$ by $2$ gives us $5$ .
So, our simplified fraction is $\frac{3}{5}$ .
Awesome!

STEP 9

$\cos M = \frac{3}{5}$ .

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QuestionIdentifying Trig Ratios (Diagram), Level 1 Score: $4 / 5$ Penalty: 1 off
Question Show
Express $\cos M$ as a fraction in simplest terms.
L But Answer Attempt 1 out of 2 7/23887042/9158711ce9be57d3a43284ce62380145

Studdy Solution

STEP 1

What is this asking? We need to find the cosine of angle $M$ in a right triangle, and write it as a simplified fraction. Watch out! Don't mix up the sides!
Make sure you're using the correct sides for the cosine calculation.

STEP 2

1. Find the hypotenuse.
2. Calculate $\cos M$ .
3. Simplify the fraction.

STEP 3

Alright, so we've got a right triangle, and we know two sides: $LM = 6$ and $LK = 8$ .
We need the hypotenuse, $MK$ , before we can find $\cos M$ .
Let's use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

STEP 4

Plugging in our values, we get $6^2 + 8^2 = MK^2$ .
This simplifies to $36 + 64 = MK^2$ , so $100 = MK^2$ .
Taking the square root of both sides gives us $MK = 10$ .
Remember, the hypotenuse is always positive!

STEP 5

Now, let's remember what cosine means: adjacent over hypotenuse.
Looking at angle $M$ , the adjacent side is $LM = 6$ , and we just found the hypotenuse, $MK = 10$ .

STEP 6

So, $\cos M = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{LM}{MK} = \frac{6}{10}$ .

STEP 7

We can simplify $\frac{6}{10}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .

STEP 8

Dividing $6$ by $2$ gives us $3$ , and dividing $10$ by $2$ gives us $5$ .
So, our simplified fraction is $\frac{3}{5}$ .
Awesome!

STEP 9

$\cos M = \frac{3}{5}$ .

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QuestionIdentifying Trig Ratios (Diagram), Level 1 Score: 4/54 / 54/5 Penalty: 1 offQuestion ShowExpress cos⁡M\cos McosM as a fraction in simplest terms.L But Answer Attempt 1 out of 2 7/23887042/9158711ce9be57d3a43284ce62380145

Studdy Solution

STEP 1

What is this asking? We need to find the cosine of angle MMM in a right triangle, and write it as a simplified fraction. Watch out! Don't mix up the sides!Make sure you're using the correct sides for the cosine calculation.

STEP 2

1. Find the hypotenuse.2. Calculate cos⁡M\cos McosM.3. Simplify the fraction.

STEP 3

Alright, so we've got a right triangle, and we know two sides: LM=6LM = 6LM=6 and LK=8LK = 8LK=8.We need the hypotenuse, MKMKMK, before we can find cos⁡M\cos McosM.Let's use the **Pythagorean theorem**: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, where aaa and bbb are the legs, and ccc is the hypotenuse.

STEP 4

Plugging in our values, we get 62+82=MK26^2 + 8^2 = MK^262+82=MK2.This simplifies to 36+64=MK236 + 64 = MK^236+64=MK2, so 100=MK2100 = MK^2100=MK2.Taking the square root of both sides gives us MK=10MK = 10MK=10.Remember, the hypotenuse is always **positive**!

STEP 5

Now, let's remember what cosine means: **adjacent over hypotenuse**.Looking at angle MMM, the adjacent side is LM=6LM = 6LM=6, and we just found the hypotenuse, MK=10MK = 10MK=10.

STEP 6

So, cos⁡M=adjacenthypotenuse=LMMK=610\cos M = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{LM}{MK} = \frac{6}{10}cosM=hypotenuseadjacent​=MKLM​=106​.

STEP 7

We can simplify 610\frac{6}{10}106​ by dividing both the numerator and the denominator by their **greatest common divisor**, which is 222.

STEP 8

Dividing 666 by 222 gives us 333, and dividing 101010 by 222 gives us 555.So, our simplified fraction is 35\frac{3}{5}53​.Awesome!

STEP 9

cos⁡M=35\cos M = \frac{3}{5}cosM=53​.

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QuestionIdentifying Trig Ratios (Diagram), Level 1 Score: $4 / 5$ Penalty: 1 off
Question Show
Express $\cos M$ as a fraction in simplest terms.
L But Answer Attempt 1 out of 2 7/23887042/9158711ce9be57d3a43284ce62380145

What is this asking? We need to find the cosine of angle $M$ in a right triangle, and write it as a simplified fraction. Watch out! Don't mix up the sides!
Make sure you're using the correct sides for the cosine calculation.

1. Find the hypotenuse.
2. Calculate $\cos M$ .
3. Simplify the fraction.

Alright, so we've got a right triangle, and we know two sides: $LM = 6$ and $LK = 8$ .
We need the hypotenuse, $MK$ , before we can find $\cos M$ .
Let's use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

Plugging in our values, we get $6^2 + 8^2 = MK^2$ .
This simplifies to $36 + 64 = MK^2$ , so $100 = MK^2$ .
Taking the square root of both sides gives us $MK = 10$ .
Remember, the hypotenuse is always positive!

Now, let's remember what cosine means: adjacent over hypotenuse.
Looking at angle $M$ , the adjacent side is $LM = 6$ , and we just found the hypotenuse, $MK = 10$ .

So, $\cos M = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{LM}{MK} = \frac{6}{10}$ .

We can simplify $\frac{6}{10}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .

Dividing $6$ by $2$ gives us $3$ , and dividing $10$ by $2$ gives us $5$ .
So, our simplified fraction is $\frac{3}{5}$ .
Awesome!

$\cos M = \frac{3}{5}$ .