Question

Find the area of the triangle. Round your answer to the nearest tenth, if necessary.

https://api.agilixbuzz.com/Resz/~Ey6YBAAAAAgn2YAMGLV7AA.5zHw-8j3BbxCE1XsQH0SjB/19809088,B84/Assets/assessmentimages/alg%202%20pt%202%20u2l9%207.jpg

90.4 in.2

140.3 in.2

70.1 in.2

80.8 in.2

Answer 1

You should find the heifht (using the angle) and the base, then apply the formula for the area:
\[A=\frac{b\cdot h}{2}\]
Or you can find the last side you don't know and apply the Heron's formula.

Answer 2

actually 70.1?

Answer 3

@John_ES

Answer 4

@jhonyy9

Answer 5

@Abhisar

Answer 6

No, the correct answer is anther one.

Answer 7

Have you find the side you don't have?

Answer 8

70.1

Answer 9

?

Answer 10

No, this is a wrong answer.

Answer 11

Ok, I will write how I would do it. Ok?

Answer 12

ok

Answer 13

First, I will calculate the side we don't have, using the cos theorem. As we have a triangle, we have 3 sides, I will name each of one this way,
a=9
c=18
b= is the unknown
The cos theorem, says that,
\[c^2=a^2+b^2-2ba\cos(C)\]
where C=60 degrees.

Answer 14

As we don't know b, we find its value, using the above relation and we find that,
\[b=20.725\ \ in\]

Answer 15

Now we can apply the Heron's formula for the area that says that,
\[A=\sqrt{s(s-a)(s-b)(s-c)}\] where s is the semiperimeter:
\[s=\frac{a+b+c}{2}\]So using this we have,
\[A=80.8\ \ in^2\]

Answer 16

so thats the answer?

Answer 17

That's the answer. You can apply the process to similar problems.