When finding the diagonal of any 45 ° 45\degree 4 5 ° right triangle, you always do what?

multiply the sides by 2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

divide the sides by 2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

When finding the side of any 45 ° 45\degree 4 5 ° right triangle, you always

divide the diagonal by 2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

multiply the diagonal by 2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

30-60-90

Presentation

•

Mathematics

•

10th Grade

•

Practice Problem

•

Medium

•

CCSS

HSG.SRT.C.8, 8.G.B.8

Standards-aligned

Anna Stevens

Used 75+ times

FREE Resource

7 Slides • 5 Questions

30-60-90

February 4, 2021

Multiple Choice

When finding the diagonal of any

45\degree

right triangle, you always do what?

multiply the sides by $\sqrt{2}$

divide the sides by $\sqrt{2}$

Multiple Choice

When finding the side of any

45\degree

right triangle, you always

multiply the diagonal by $\sqrt{2}$

divide the diagonal by $\sqrt{2}$

30 - 60 - 90 right triangles

These numbers refer to the angle measures of a right triangle

Evaluating a 30-60-90 triangle

The short leg is always between the 60 and 90. This leg is always the one we use to measure.
The long leg is always
$\sqrt{3}$ times longer than the short leg
The hypotenuse (diagonal) is always twice the short leg

Multiple Choice

Given that 5 is the short leg, what is the length of the long leg, b?

$5\sqrt{3}$

$\sqrt{15}$

$3\sqrt{5}$

not enough information

b = $5\sqrt{3}$

To find the long leg: take the length of the short leg and multiply it by $\sqrt{3}$

Multiple Choice

Given that 5 is the short leg, what is the length of the hypotenuse, c?

$\sqrt{10}$

$5\sqrt{2}$

not enough information

c = 10

To find the hypotenuse, take the length of the short side and double it.

Find n and m

Since 12 is the hypotenuse, we know that 12 = 2n (because the hypotenuse is always 2 times the short leg
Know that 12 = 2n
divide by 2
n = 6
$m=n\sqrt{3}$
$m=6\sqrt{3}$

Open Ended

Find y and x

Type response here

Find x and y

$y=\frac{44}{2}=22$
$x=y\sqrt{3}=22\sqrt{3}$

30-60-90

February 4, 2021

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