Question

IF YOU CAN HELP WITH EITHER ILL BE SO THANKFUL I HAVE A TEST TOMORROW a. The diagonals of a rectangle are 8 units long and intersect at a 60 degree angle. Find the dimensions of the rectangle.
b. The perimeter of a rhombus is 64 and one of its angles has a measure of 120. Find the lengths of the diagonals

Answer 1

I think the trick for the first one (a) is to use 30-60-90 triangles... but, have you learned that concept at any point in your course? :)

Answer 2

that's better

Answer 3

so can you tell what the width is?

Answer 4

yes @jtvatsim but idk how to do this problem

Answer 5

oh okay @jdoe0001 thanks

Answer 6

so the 2x side is 4, thus the "x" side will be half that

Answer 7

ohh one sec... darn the hypotenuse is not 4... alright lemme do this

Answer 8

\(\bf x\sqrt{3}={\color{blue}{ 4}}\implies x=\cfrac{{\color{blue}{ 4}}}{\sqrt{3}}\implies \cfrac{4\sqrt{3}}{3}\)

Answer 9

you'd use also the 30-90-60 rule

Answer 10

that'd be the rhombus
so to find the diagonals length

notice the right triangle, the blue lines are half of each diagonal
so once you find those 2, the diagonals will be twice as much

Answer 11

\(\bf 2x={\color{blue}{ 16}} \implies x=\cfrac{16}{2}\implies x={\color{red}{ 8}} \iff \textit{shorter side}
\\ \quad \\
x\sqrt{3}\implies {\color{red}{ 8}}\sqrt{3} \iff \textit{longer side}
\\ \quad \\ \quad \\
\textit{shorter diagonal}=2\cdot {\color{red}{ 8}}\implies 16
\\ \quad \\
\textit{longer diagonal}=2\cdot {\color{red}{ 8}}\sqrt{3}\implies 16\sqrt{3}\)

Answer 12

@jim_thompson5910 can you try explaining the first one to me? i dont understand it

Answer 13

This one? "a. The diagonals of a rectangle are 8 units long and intersect at a 60 degree angle. Find the dimensions of the rectangle. "

or something else?

Answer 14

yes that

Answer 15

i think i got it idk if its right though

Answer 16

i got the side across 90 degrees= 16
the side across 30 degrees= 8 radical 3/3
the side across 60 degrees=8

Answer 17

@jim_thompson5910

Answer 18

Ok let's start off with a drawing

Answer 19

One property you can prove about rectangles is that the diagonals are congruent. Another thing you can show is the diagonals cut each other in half. Because the diagonals are both 8 units, this means they cut each other into 4 unit pieces like this