Question

What is the area of triangle ABC if a = 19, b = 14, and c = 23? in unites.

Answer 1

I've had these questions multiple times, and I still don't know how to do it, so an explanation with it please.

Answer 2

Have you heard of Heron's formula?

Answer 3

I was assigned pre-cal without every knowing how to do it, so no.

Answer 4

Heron's formula is a simple formula that gives you the area of a triangle given all its sides.

Answer 5

For a triangle with side lengths a, b, and c, the area is

\(A = \sqrt{s(s - a)(s - b)(s - c)} \)

where \(s = \dfrac{a + b + c }{2} \)

Answer 6

What is s ?

Answer 7

Read the entire response above.

Answer 8

Oh okay, I got it, thank you.

Answer 9

Let me plug in, and I'll let you know what I got.

Answer 10

132.82 is the answer.

Answer 11

@mathstudent55 I have another question similar to this, but it's asking for degree, could you give me the formula for it?

Answer 12

In triangle ABC, what is the measure of A if a = 9, b = 14, and c = 8?

Answer 13

Correct. A = 132.8

Answer 14

For the second question, since you have the measures of all sides but no angles, you need to use the law of cosines.

\(a^2 = b^2 + c^2 - 2bc \cos A\)

Answer 15

You know a, b, and c. The only unknown is A, which you can solve for using the inverse cosine function.

Answer 16

Let me see if I can get this one, but I want double assurance.

Answer 17

Wait how would I solve if I don't know what A is?

Answer 18

First, replace all variables with their known values, leaving only A as A since you don't know it.
Then solve for cos A.

Answer 19

So I don't plug in cos A with the equation?

Answer 20

9^2=14^2+8^2-2(14)(8) cos A

Answer 21

\(a^2 = b^2 + c^2 - 2bc \cos A\)

\(9^2 = 14^2 + 8^2 - 2\times 14 \times 8 \cos A\)

You understand it so far?

Answer 22

Correct.

Answer 23

Now do the squares, and multiply together the numbers that multiply the cos A.

Answer 24

So I multiply cos A last?

Answer 25

81=260-224 cos A

Answer 26

Treat cos A as x, an unknown amount.

\(81 = 196 + 64 - 224 \cos A\)

\(81 = 260 - 224 \cos A\)

Correct.

Answer 27

We are solving for cos A.
Now subtract 260 from both sides.

Answer 28

224cos A=179?

Answer 29

So 81=260-179.

Answer 30

But that doesn't give me the degree.

Answer 31

\(179 = 224 \cos A\)

Now divide both sides by 224

\(\cos A = \dfrac{179}{224} \)

Answer 32

We're getting there.

Answer 33

Now we have solved for cos A, ok?

Answer 34

0.799

Answer 35

Now we use the inverse cosine function, which may be called \(\cos^{-1} \) in your calculator.

Answer 36

So, Cos 0.799?

Answer 37

Cos A= 0.799.

Answer 38

Angle A has a cosine of 0.799.
Now we want to know what angle A is.
Do inverse cosine of 0.799.

Answer 39

Your last line is correct. the previous one is not.

Answer 40

You need to do \(\cos^{-1} 0.799 = \)

Answer 41

cos^-1 0.799?

Answer 42

0.645.

Answer 43

Which is 36.97 degree.

Answer 44

I don't know what you mean by 0.645, but A = 36.955 deg is correct.

Answer 45

0.645 was result in radians.

Answer 46

Thank you!

Answer 47

Ok.
You're welcome.

Answer 48

BTW, if you need the other angles of this triangle, now you can use the law of sines to find the next angle. Then you can use the theorem that states that the sum of the measures of the angles of a triangle is 180 to find the last angle.

Answer 49

Thank you, I'll refer back to this multiple times.

Answer 50

You're welcome.