!!! find the indicated side of the triangle PLZ HELP

a=17√2

Step-by-step explanation:

Hi there!

We are given a right triangle with the measure of one angle being 45°, and one of the sides being measured 17

we need to find a

first, let's find the measure of the other angle

because it's a right triangle, the sum of the acute angles are complementary, meaning they add up to 90°

let's make the unknown degree of the other angle x

so that means to find x:

45+x=90

subtract 45 from both sides

x=45°

that means the measure of the other angle is 45°

You may notice since we have two angles with the same measure, that means this triangle is isosceles.

That means the other leg (the other side that isn't marked) is also 17

of course, you could solve for a using Pythagorean theorem, but there's actually a shortcut:

in 45°-45°-90°Δ, the legs are a specific value, and the hypotenuse (the side opposite from the 90° is the value of the legs*√2 (for example, if the legs are 3, then the hypotenuse is 3√2). To remember the rule, if the legs have a measure of s, the hypotenuse has a measure of s√2

therefore the measure of a is 17√2

Hope this helps!

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: