Question

Need help ASAP!!

A triangle has side lengths of 34 in., 20 in., and 47 in. Is the triangle acute, obtuse or right?
A. right
B. obtuse
C. acute

For the answer I got B. obtuse. Is it correct?

16. A triangle has side lengths of 1.2, 4.6 and 5. Determine if the triangles is Acute, Obtuse, or Right.

For the answer I got Acute. Is it correct?

17. Find the value of x.

Picture 1 is my work for number 11.
Picture 2 is my work for number 16.
Picture 3 is what I need to use to solve for x.

Answer 1

1. B (obtuse)

2. Obtuse

3. 20.92

Explanation:

1.

We need to use the converse of the pythagorean theorem to solve this problem. Given that c is the longest side of a triangle, and a and b are the other two sides. The triangle is right triangle if
`c^2=a^2 +b^2`

The triangle is acute triangle if
`c^2 < a^2 + b^2`

The triangle is obtuse triangle if
`c^2 > a^2 + b^2`

the longest side of this triangle is 47, so we check:

`47^2=2209`, and

`34^2 + 20 ^2 =1556`

Hence, c^2 is GREATER than a^2 + b^2, so the triangle is obtuse.

2. Using the points we showed above, we can again summarize:

• If
  `c^2 = a^2 + b^2` -- Right Triangle
• if
  `c^2 < a^2 + b^2` -- Acute Triangle
• if
  `c^2 > a^2 + b^2` -- Obtuse Triangle

This triangle's c (longest side) is 5. Let's check:

5^2 = 25, and

`(1.2)^2 + (4.6) ^2=22.6`

Hence, c^2 is GREATER than a^2 +b^2, so the triangle is obtuse.

3.

The side opposite of the 90 degree angle is the "hypotenuse", that is x. The side opposite the 35 degree angle is "opposite" side.

The trigonometric ratio that related "opposite" side to "hypotenuse" side is SINE. So we can write:

`Sin(35)=(Opposite)/(Hypotenuse)\\Sin(35)=(12)/(x)`

Now, cross multiplying and solving:

`Sin(35)=(12)/(x)\\x*Sin(35)=12\\x=(12)/(Sin(35))\\x=20.92`