Math / Trigonometry

QuestionGiven the triangle $10.875 \quad 17$ , find the measure of angle $A$ using the Law of Cosines. Picture is not drawn to scale $A=$ $\square$ degrees

Studdy Solution

STEP 1

1. The triangle is a non-right triangle.
2. The sides of the triangle are labeled as $a = 10.875$ , $b = 17$ , and $c = 21.62517$ .
3. Angle $A$ is opposite side $c$ .

STEP 2

1. Recall the Law of Cosines formula.
2. Substitute the given side lengths into the formula.
3. Solve for $\cos A$ .
4. Use the inverse cosine function to find angle $A$ .

STEP 3

Recall the Law of Cosines formula:
$c^2 = a^2 + b^2 - 2ab \cdot \cos A$

STEP 4

Substitute the given side lengths into the formula:
$(21.62517)^2 = (10.875)^2 + (17)^2 - 2 \times 10.875 \times 17 \times \cos A$

STEP 5

Calculate the squares of the side lengths:
$21.62517^2 = 467.625$ $10.875^2 = 118.265625$ $17^2 = 289$
Substitute these values back into the equation:
$467.625 = 118.265625 + 289 - 2 \times 10.875 \times 17 \times \cos A$
Simplify the equation:
$467.625 = 407.265625 - 369.75 \cdot \cos A$
Rearrange to solve for $\cos A$ :
$467.625 - 407.265625 = -369.75 \cdot \cos A$
$60.359375 = -369.75 \cdot \cos A$
$\cos A = \frac{60.359375}{-369.75}$
$\cos A \approx -0.1633$

STEP 6

Use the inverse cosine function to find angle $A$ :
$A = \cos^{-1}(-0.1633)$
Calculate angle $A$ :
$A \approx 99.4^\circ$
The measure of angle $A$ is:
$\boxed{99.4^\circ}$

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QuestionGiven the triangle $10.875 \quad 17$ , find the measure of angle $A$ using the Law of Cosines. Picture is not drawn to scale $A=$ $\square$ degrees

Studdy Solution

STEP 1

1. The triangle is a non-right triangle.
2. The sides of the triangle are labeled as $a = 10.875$ , $b = 17$ , and $c = 21.62517$ .
3. Angle $A$ is opposite side $c$ .

STEP 2

1. Recall the Law of Cosines formula.
2. Substitute the given side lengths into the formula.
3. Solve for $\cos A$ .
4. Use the inverse cosine function to find angle $A$ .

STEP 3

Recall the Law of Cosines formula:
$c^2 = a^2 + b^2 - 2ab \cdot \cos A$

STEP 4

Substitute the given side lengths into the formula:
$(21.62517)^2 = (10.875)^2 + (17)^2 - 2 \times 10.875 \times 17 \times \cos A$

STEP 5

STEP 6

Use the inverse cosine function to find angle $A$ :
$A = \cos^{-1}(-0.1633)$
Calculate angle $A$ :
$A \approx 99.4^\circ$
The measure of angle $A$ is:
$\boxed{99.4^\circ}$

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QuestionGiven the triangle 10.8751710.875 \quad 1710.87517, find the measure of angle AAA using the Law of Cosines. Picture is not drawn to scale A=A=A= □\square□ degrees

Studdy Solution

STEP 1

1. The triangle is a non-right triangle.2. The sides of the triangle are labeled as a=10.875 a = 10.875 a=10.875, b=17 b = 17 b=17, and c=21.62517 c = 21.62517 c=21.62517.3. Angle A A A is opposite side c c c.

STEP 2

1. Recall the Law of Cosines formula.2. Substitute the given side lengths into the formula.3. Solve for cos⁡A\cos AcosA.4. Use the inverse cosine function to find angle A A A.

STEP 3

Recall the Law of Cosines formula:c2=a2+b2−2ab⋅cos⁡A c^2 = a^2 + b^2 - 2ab \cdot \cos A c2=a2+b2−2ab⋅cosA

STEP 4

Substitute the given side lengths into the formula:(21.62517)2=(10.875)2+(17)2−2×10.875×17×cos⁡A (21.62517)^2 = (10.875)^2 + (17)^2 - 2 \times 10.875 \times 17 \times \cos A (21.62517)2=(10.875)2+(17)2−2×10.875×17×cosA

STEP 5

STEP 6

Use the inverse cosine function to find angle A A A:A=cos⁡−1(−0.1633) A = \cos^{-1}(-0.1633) A=cos−1(−0.1633)Calculate angle A A A:A≈99.4∘ A \approx 99.4^\circ A≈99.4∘ The measure of angle A A A is:99.4∘ \boxed{99.4^\circ} 99.4∘​

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QuestionGiven the triangle $10.875 \quad 17$ , find the measure of angle $A$ using the Law of Cosines. Picture is not drawn to scale $A=$ $\square$ degrees

1. The triangle is a non-right triangle.
2. The sides of the triangle are labeled as $a = 10.875$ , $b = 17$ , and $c = 21.62517$ .
3. Angle $A$ is opposite side $c$ .

1. Recall the Law of Cosines formula.
2. Substitute the given side lengths into the formula.
3. Solve for $\cos A$ .
4. Use the inverse cosine function to find angle $A$ .

Recall the Law of Cosines formula:
$c^2 = a^2 + b^2 - 2ab \cdot \cos A$

Substitute the given side lengths into the formula:
$(21.62517)^2 = (10.875)^2 + (17)^2 - 2 \times 10.875 \times 17 \times \cos A$

Use the inverse cosine function to find angle $A$ :
$A = \cos^{-1}(-0.1633)$
Calculate angle $A$ :
$A \approx 99.4^\circ$
The measure of angle $A$ is:
$\boxed{99.4^\circ}$