Question

SOMEONE PLEASE HELP ME! I have a few of the explanations but I'm not sure if I need more please suggest some thank you

Here are 3 different triangles with different missing side and/or angle measures (not to scale). For each triangle, explain what you can and cannot solve for.
For each thing you cannot find, explain whether or you think there is only one value it can be (but you just don't have a way to find it yet) or whether you think there isn't enough information for there to be just one right answer for the missing information.
For the things you do know how to find, explain which tool or fact about triangles you would use to solve it. (You do not need to find the missing values themselves.)

Answer 1

For tingle #1

We can find angle C using the triangle sum theorem: the three interior angles of any triangle add up to 180 degrees. Since we know the measures of angles A and B, we can find C.

`C=180-(A+B)`

`C=180-(21.24+27.14)`

`C=131.62`

We cannot find any of the sides. Since there is noting to show us size, there is simply just not enough information; we need at least one side to use the rule of sines and find the other ones. Also, since there is nothing showing us size, each side can have more than one value.

For triangle #2

In this one, we can find everything and there is one one value for each.

- We can find side c

Since we have a right triangle, we can find side c using the Pythagorean theorem

`b^2=a^2+c^2`

`4^2=2^2+c^2`

`16=4+c^2`

`12=c^2`

`c=√(12)`

`c=2√(3)`

- We can find angle C using the cosine trig identity

`cos(C)=(adjacent)/(hypotenuse)`

`cos(C)=(2)/(4)`

`C=arccos((2)/(4) )`

`C=60`

- Now we can find angle A using the triangle sum theorem

`A=180-(B+C)`

`A=180-(90+60)`

`A=30`

For triangle #3

Again, we can find everything and there is one one value for each.

- We can find angle A using the triangle sum theorem

`A=180-(B+C)`

`A=180-(90+34.88)`

`A=55.12`

- We can find side a using the tangent trig identity

`tan(C)=(opposite-side)/(adjacent-side)`

`tan(34.88)=(7)/(a)`

`a=(7)/(tan(34.88))`

`a=10.04`

- Now we can find side b using the Pythagorean theorem

`b^2=a^2+c^2`

`b^2=10.04^2+7^2`

`b^2=149.8`

`b=√(149.8)`