In Exercises 1-12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state “no triangle.” If two triangles exist, solve each triangle. A = 70 ∘ , B = 55 ∘ , a = 12

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Answer 1

Textbook Question

Chapter 6, Problem 1RE

In Exercises 1-12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state “no triangle.” If two triangles exist, solve each triangle.

$A = 70 ∘ , B = 55 ∘ , a = 12$

Expert Solution & Answer

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

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Answer 2

Textbook Question

Chapter 6, Problem 1RE

In Exercises 1-12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state “no triangle.” If two triangles exist, solve each triangle.

$A = 70 ∘ , B = 55 ∘ , a = 12$

Expert Solution & Answer

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

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Answer 3

Textbook Question

Chapter 6, Problem 1RE

In Exercises 1-12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state “no triangle.” If two triangles exist, solve each triangle.

$A = 70 ∘ , B = 55 ∘ , a = 12$

Expert Solution & Answer

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

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Answer 4

Textbook Question

Chapter 6, Problem 1RE

In Exercises 1-12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state “no triangle.” If two triangles exist, solve each triangle.

$A = 70 ∘ , B = 55 ∘ , a = 12$

Expert Solution & Answer

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

Answer 8

Expert Solution & Answer

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To calculate: The length of triangle to the nearest tenth and angle measure to the nearest degree whose angles and side is $A=70°,B=55°,a=12$ .

Answer 12

Answer to Problem 1RE

Solution: The missing values are: $C=55°,b≈10.4 and c≈10.5$

Answer 13

Explanation of Solution

Given Information: The values: $A=70°,B=55°,a=12$ .

Formula used:

$asinA=bsinB=csinC$ .

$a2=b2+c2−2⋅b⋅c⋅cosAb2=a2+c2−2⋅a⋅c⋅cosBc2=a2+b2−2⋅a⋅b⋅cosC$

Calculation:

For any triangle,

The Law of sine states:

$asinA=bsinB=csinC$

Using the angle sum property we will obtain:

$A+B+C=180°70°+55°+C=180°C=180°−125°C=55°$

Using the law of sines we get,

$asinA=csinC12sin70°=csin55°c⋅sin70°=12⋅sin55°c=12⋅sin55°sin70°$

This gives $c≈10.5$ to the nearest tenth.

Also,

$asinA=bsinB12sin70°=bsin55°b⋅sin70°=12⋅sin55°b=12⋅sin55°sin70°$

This gives $b≈10.5$ to the nearest tenth.

So, $C=55°,b≈10.4 and c≈10.5$ .

Hence, $C=55°,b≈10.4 and c≈10.5$ .

Answer 14

Ch. 6.1 - Check Point 1 Solve the triangle shown in Figure...Ch. 6.1 - Check Point 2 Solve triangle ABC if A=40,C=22.5,...Ch. 6.1 - Check Point 3 Solve triangle ABC if A = 57 a = 33,...Ch. 6.1 - Check Point 4 Solve triangle ABC if A = 50, a =...Ch. 6.1 - Prob. 5CP Ch. 6.1 - Check Point 6 Find the area of a triangle having...Ch. 6.1 - Check Point 7 Two fire-lookout stations are 13...Ch. 6.1 - Prob. 1CVC Ch. 6.1 - Prob. 2CVC Ch. 6.1 - Prob. 3CVC

In Exercises 1-12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state “no triangle.” If two triangles exist, solve each triangle. A = 70 ∘ , B = 55 ∘ , a = 12

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Answer to Problem 1RE

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