Math / Trigonometry

Question $\tan A$ in this figure is $\qquad$ a $\frac{4}{3}$ b $\frac{3}{5}$
C $\frac{3}{4}$ d $\frac{4}{5}$

Studdy Solution

STEP 1

1. We are dealing with a right triangle.
2. The sides of the triangle are labeled 18, 24, and 30.
3. Angle $A$ is opposite the side measuring 18.
4. Angle $A$ is adjacent to the side measuring 24.
5. We need to find $\tan A$ .

STEP 2

1. Identify the opposite and adjacent sides relative to angle $A$ .
2. Use the definition of tangent for a right triangle.
3. Calculate $\tan A$ using the identified sides.
4. Compare the calculated value with the given options.

STEP 3

Identify the opposite and adjacent sides relative to angle $A$ :
- The opposite side to angle $A$ is 18. - The adjacent side to angle $A$ is 24.

STEP 4

Use the definition of tangent for a right triangle:
$\tan A = \frac{\text{opposite side}}{\text{adjacent side}}$

STEP 5

Calculate $\tan A$ using the identified sides:
$\tan A = \frac{18}{24}$
Simplify the fraction:
$\tan A = \frac{3}{4}$

STEP 6

Compare the calculated value with the given options:
- Option a: $\frac{4}{3}$ - Option b: $\frac{3}{5}$ - Option c: $\frac{3}{4}$ - Option d: $\frac{4}{5}$
The calculated value $\frac{3}{4}$ matches option c.
The value of $\tan A$ is:
$\boxed{\frac{3}{4}}$

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Question $\tan A$ in this figure is $\qquad$ a $\frac{4}{3}$ b $\frac{3}{5}$
C $\frac{3}{4}$ d $\frac{4}{5}$

Studdy Solution

STEP 1

1. We are dealing with a right triangle.
2. The sides of the triangle are labeled 18, 24, and 30.
3. Angle $A$ is opposite the side measuring 18.
4. Angle $A$ is adjacent to the side measuring 24.
5. We need to find $\tan A$ .

STEP 2

1. Identify the opposite and adjacent sides relative to angle $A$ .
2. Use the definition of tangent for a right triangle.
3. Calculate $\tan A$ using the identified sides.
4. Compare the calculated value with the given options.

STEP 3

Identify the opposite and adjacent sides relative to angle $A$ :
- The opposite side to angle $A$ is 18. - The adjacent side to angle $A$ is 24.

STEP 4

Use the definition of tangent for a right triangle:
$\tan A = \frac{\text{opposite side}}{\text{adjacent side}}$

STEP 5

Calculate $\tan A$ using the identified sides:
$\tan A = \frac{18}{24}$
Simplify the fraction:
$\tan A = \frac{3}{4}$

STEP 6

Compare the calculated value with the given options:
- Option a: $\frac{4}{3}$ - Option b: $\frac{3}{5}$ - Option c: $\frac{3}{4}$ - Option d: $\frac{4}{5}$
The calculated value $\frac{3}{4}$ matches option c.
The value of $\tan A$ is:
$\boxed{\frac{3}{4}}$

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Questiontan⁡A\tan AtanA in this figure is \qquad a 43\frac{4}{3}34​ b 35\frac{3}{5}53​C 34\frac{3}{4}43​ d 45\frac{4}{5}54​

Studdy Solution

STEP 1

1. We are dealing with a right triangle.2. The sides of the triangle are labeled 18, 24, and 30.3. Angle A A A is opposite the side measuring 18.4. Angle A A A is adjacent to the side measuring 24.5. We need to find tan⁡A\tan AtanA.

STEP 2

1. Identify the opposite and adjacent sides relative to angle A A A.2. Use the definition of tangent for a right triangle.3. Calculate tan⁡A\tan AtanA using the identified sides.4. Compare the calculated value with the given options.

STEP 3

Identify the opposite and adjacent sides relative to angle A A A:- The opposite side to angle A A A is 18. - The adjacent side to angle A A A is 24.

STEP 4

Use the definition of tangent for a right triangle:tan⁡A=opposite sideadjacent side\tan A = \frac{\text{opposite side}}{\text{adjacent side}}tanA=adjacent sideopposite side​

STEP 5

Calculate tan⁡A\tan AtanA using the identified sides:tan⁡A=1824\tan A = \frac{18}{24}tanA=2418​Simplify the fraction:tan⁡A=34\tan A = \frac{3}{4}tanA=43​

STEP 6

Compare the calculated value with the given options:- Option a: 43\frac{4}{3}34​ - Option b: 35\frac{3}{5}53​ - Option c: 34\frac{3}{4}43​ - Option d: 45\frac{4}{5}54​The calculated value 34\frac{3}{4}43​ matches option c. The value of tan⁡A\tan AtanA is:34\boxed{\frac{3}{4}}43​​

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Question $\tan A$ in this figure is $\qquad$ a $\frac{4}{3}$ b $\frac{3}{5}$
C $\frac{3}{4}$ d $\frac{4}{5}$

1. We are dealing with a right triangle.
2. The sides of the triangle are labeled 18, 24, and 30.
3. Angle $A$ is opposite the side measuring 18.
4. Angle $A$ is adjacent to the side measuring 24.
5. We need to find $\tan A$ .

1. Identify the opposite and adjacent sides relative to angle $A$ .
2. Use the definition of tangent for a right triangle.
3. Calculate $\tan A$ using the identified sides.
4. Compare the calculated value with the given options.

Identify the opposite and adjacent sides relative to angle $A$ :
- The opposite side to angle $A$ is 18. - The adjacent side to angle $A$ is 24.

Use the definition of tangent for a right triangle:
$\tan A = \frac{\text{opposite side}}{\text{adjacent side}}$

Calculate $\tan A$ using the identified sides:
$\tan A = \frac{18}{24}$
Simplify the fraction:
$\tan A = \frac{3}{4}$

Compare the calculated value with the given options:
- Option a: $\frac{4}{3}$ - Option b: $\frac{3}{5}$ - Option c: $\frac{3}{4}$ - Option d: $\frac{4}{5}$
The calculated value $\frac{3}{4}$ matches option c.
The value of $\tan A$ is:
$\boxed{\frac{3}{4}}$