Question

Need help on geometry Please

Answer 1

1. To find this we are going to use the converse of the Pythagorean theorem: if the square of the longest side of a triangle is equal to the sum of the squares of its smaller side, the triangle is a right one.
We know from our picture that the longer side of the triangle is 36 and its shorter sides are 24 and 15.
$36^2=24^2+15^2$
$1296=576+225$
$1296 \neq 801$
The converse also says that if the square of the longest side is greater than the sum of the squares of the shorter sides, the triangle is obtuse, and if the square of the longest side less than the sum of the squares of the shorter sides, the triangle is acute.
$1296\ \textgreater \ 801$ 

We can conclude that our triangle is an obtuse one; the correct answer is the third one: obtuse

2. Here we have a right triangle with longer side 80 feet and one of the shorter sides 65 feet. Lest $x$ be the distance from the base to the guy wire attached point.
Using the Pythagorean theorem:
$80^2=65^2+x^2$
$x^2=80^2-65^2$
$x= \sqrt{80^2-65^2}$
$x=46.64$

We can conclude that the correct answer is fourth choice: 46.64

3. Here we are going to use the Pythagorean theorem. We know that the longest side of our triangle is 40 and its shorter sides are 9 and $x$. Using the Pythagorean theorem:
$40^2=9^2+x^2$
$x^2=40^2-9^2$
$x= \sqrt{40^2-9^2}$
$x=38.97$

We can conclude that the correct answer is the fourth option: 38.97