# A triangle has sides with the following lengths: AB=3, BC=4, CA=5. Which angle is the smallest?

## Answers

Answer 1
Answer:

Answer:

A = 36.9°

Step-by-step explanation:

In this triangle we know the three sides:

AB = 3,

BC = 4 and

CA = 5.

Use The Law of Cosines first to find angle A first:

cos A = (BC² + CA² − AB²) / 2BCCA

cos A = (4² + 5² − 3²) / (2×4×5)

cos A = (16 + 25 − 9) / 40

cos A = 0.80

A = cos⁻¹(0.80)

A = 36.86989765°

A = 36.9° to one decimal place.

Next we will find another side. We use The Law of Cosines again, this time for angle B:

cos B = (CA² + AB² − BC²) / 2CAAB

cos B = (5² + 3² − 4²) / (2×5×3)

cos B = (25 + 9 − 16) / 30

cos B = 0.60

B = cos⁻¹(0.60)

B = 53.13010235°

B = 53.1° to one decimal place

Finally, we can find angle C by using 'angles of a triangle add to 180°:

C = 180° − 36.86989765° − 53.13010235°

C = 90°

Now we have completely solved the triangle i.e. we have found all its angles.

So we can analyze from above that the smallest angle in the triangle ABC is A with 36.9°.

## Related Questions

Give an equality that represents the phrase the sum 1 and y is greater than or equal to 9.

### Answers

That would be 1+y≥9

the one and the y go on one side and the nine on the other

Which of the sequences is an arithmetic sequence? A. 154, 71, 8, 5, 2, ... B. 12, –24, 36, –48, 60, ... C. 1, 5, 10, 15, 20, ... D. –20, –27, –34, –41, –48, ..

### Answers

D, it decreases by -7 while the other options are multiplied to get the next number

Answer:

D

Step-by-step explanation:

How do I find the answer to this question 3/5m=9 can you show me step by step

### Answers

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3/5m=9 One solution was found :                   m = 15

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3/5*m-(9)=0

Step by step solution : Step  1  : 3 Simplify — 5 Equation at the end of step  1  : 3 (— • m) - 9 = 0 5 Step  2  :Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

9 9 • 5 9 = — = ————— 1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3m - (9 • 5) 3m - 45 ———————————— = ——————— 5 5 Step  3  :Pulling out like terms :

3.1     Pull out like factors :

3m - 45  =   3 • (m - 15)

Equation at the end of step  3  : 3 • (m - 15) ———————————— = 0 5 Step  4  :When a fraction equals zero : 4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

3•(m-15) ———————— • 5 = 0 • 5 5

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
3  •  (m-15)  = 0

Equations which are never true :

4.2      Solve :    3   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3      Solve  :    m-15 = 0

Add  15  to both sides of the equation :
m = 15

One solution was found :                   m = 15

William's yard has a perimeter of 2 2/6. The length is 3/6. What is the width?

### Answers

I really don’t know, can you ask someone such as your mother/father or an older sibling? May help.