Answer:
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!
