Question

HELP PLEASEEEEE
3. Given a right triangle DEF with angle D as a right angle, find side DE if DF = 5 units and EF = 13 units.

4. Given a right triangle PQR with angle R as 90 degrees and angle Q as 54 degrees, find side PR if side RQ is 4.6 units.

5. Given a right triangle ABC with angle C as 90 degrees, find angle A if side AC = 3.0 units and BC = 6.8 units and AC = 3.0 units, find angle A.

Answer 1

Pleaseeee helppp

Answer 2

@jhonyy9 @kittybasil

Answer 3

@Ultrilliam @Vocaloid

Answer 4

just you need use Pythagora's theorem - hope you know it

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @jhonyy9
just you need use Pythagora's theorem - hope you know it
\(\color{#0cbb34}{\text{End of Quote}}\)
I am not sure but thanks anyway!

Answer 6

what say the Pythagora's theorem ?

Answer 7

@llamalover777 The Pythagoras Theorem is as such:\[a^{2}+b^{2}=c^{2}\]where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse (longest side) of a right-angle triangle. A triangle like the one you've been given. As is, we are trying to find the second leg, which I will call "b" for convenience.

Here's what info you have so far:
\(a=5\), \(c=13\)

Let's plug that into the equation:\[(5)^{2}+b^{2}=(13)^{2}\]Now we need to simplify this. Our end goal is to isolate (get alone) the \(b\) variable so you will know its value as the length of the second leg. Therefore:\[25+b^{2}=169\]\[b^{2}=169-25=144\]

Answer 8

Now we have the following:\[b^{2}=144\]To get the variable \(b\) alone, we need to square root both sides:\[\sqrt{b^2}=\sqrt{144}\]\[\therefore b=\sqrt{144}=\pm12\]As a result, the length of the second leg is 12 units.

Why do we ignore the negative half of the pair? You cannot have a negative length value.
Hope that helped.