Need

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.

1. B (obtuse)

2. Obtuse

3. 20.92

Step-by-step 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  

The triangle is acute triangle if  

The triangle is obtuse triangle if  

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

, and

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:

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

5^2 = 25, and

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:

Now, cross multiplying and solving:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b