If the hypotenuse of a 45°-45°-90° triangle has a length

Brennan Flores 2021-08-16 Answered

If the hypotenuse of a 45°-45°-90° triangle has a length of

\sqrt 2

, how long are the legs?

Ask Expert 1 See Answers

You can still ask an expert for help

Expert Answer

Velsenw

Answered 2021-08-17 Author has 91 answers

A 45°-45°-90° triangle is a right isosceles triangle. If x is the length of each leg, we can use the Pythagorean Theorem to write:

x^{2} + x^{2} = {(\sqrt 2)}^{2}

2 x^{2} = 2

x^{2} = 1

x=1

This is helpful

This is helpful 2

You might be interested in

asked 2022-06-03

Verify this identity:

\sin 6 α + \sin 2 α = \frac{\cos^{2} 2 α - \cos 2 α \cos 6 α}{\sin 2 α}

See answers (2)

asked 2021-12-17

\cot 0

See answers (3)

asked 2021-12-26

\sin (\frac{π}{3})

See answers (3)

asked 2021-09-06

if $x = 2, f (x) = 1$
if $x = 3, f (x) = 4$
if $x = 5, f (x) = - 2$
if $x = 8, f (x) = 3$
if $x = 13, f (x) = 6$
f is twice variable for all real numbers.
1. Find $f^{'} (4)$
2. Approximate ${\int_{2}}^{13} f^{'} (x) d x$
2. Find the value of ${\int_{2}}^{8} (3 - f^{'} (x)) d x$

See answers (1)

asked 2021-08-19

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation θ.

$θ = \frac{π}{3}$

See answers (1)

asked 2021-12-10

| a - b | \geq | a | - | b |

See answers (2)

asked 2021-02-10

Given a triangle with angle coordinates:
A(0,0), B(3,4), C(7,1)
Prove that

△ A B C

See answers (1)

New questions

Find the average area of all circles centered at the origin with radii between 1 and 3.

The perimeter of a triangle is 76cm. Side a of triangle is twice as long as side b. side c is 1cm longer than side a. find the length of each side.

\tan x - \sin x = (\tan x (\sin x)^{2}) / (\cos x + 1)

A prismatoid has a square and an equilateral triangular bases whose edges measure 3 cm each. If the midsection is 5 cm2 and the altitude of the solid is 6 cm, find the volume of the solid.

1.the length of a rectangle is 3 in. more than the width. if the perimeter is 30 in., find the area of a rectangle.
2.a square has an area of

16 y d^{2}

. what is the perimeterof the square?
3.The area of a triangle is

112 m^{2}

. If the length of thebase is 16 m, what is the height?
4.What is the maximum area for a rectangle with a perimeter of 40centimeters?
5.The length of a rectangle is 2 in. more than the width. If the perimeter is 24 in., find the area of the rectangle.

This sort of question I'm more checking if I'm doing itcorrectly, its been awhile since I've done something like this,always need a refresher anyways the question(s) is...
E. Coli cells are about

2 μ

0.8 μ

m indiameter:
How many E. Coli cells laid end to end would fit across thediameter of the pinhead, assuming the pinhead diameter of 0.5 mm,and what would be the volume of an E.Coli cell assuming that its acylinder.
Ok, what I've done was simple I guess, the first part whichI've assumed that "long" ment length, and I've taken the longestpart of E. Coli and did the idea of

0.5 \times 10^{- 3} m / 2.0 \times 10^{- 6} m = 250

Cellsgoing across.
[Wasn't sure if it was suppose to use the othernumber, just assuming it was talking about long ways]
For the second part of the question, I just used the formulaof

V = π r^{2} h

in which I came up with

V = (3.14) (0.4 \times 10^{- 6} m) 2 (2.04 \times 10^{- 6} m) = 1.00 \times 10^{- 18} m

Which something doesn't seem correct, or atleast seems oddto me.
Also, I don't know if I'm pushing the amount of questions Ican ask in a single problem, but the next part its asking for the Surface area of an E. Coli cell, and what is the surface to volumeratio of an E. Coli cell?
Which I have no idea, what type of surface area I should usefor a cell, then do I just compare the volume to the surface area,that I got in the previous problem?

θ \in [π / 2, π]

\tan θ = 1 / 3

\sin θ

\cos θ

(but to find the angle is not needed)

Choose 3 inequalities that form a system whose graph is the shaded region shown above.

A . y \leq - 2 B . y \geq - 2 C . 7 x - 4 y \geq - 13 D . 7 x + 2 y \geq 17 E . 7 x - 4 y \leq - 13 F . 7 x + 2 y \leq 17 G . x \geq - 2 H . y \leq 2

Show that every two blocks have at most one vertex in common

Create a nest of 5 sets whose largest set in the set of all polygons. For each set but the largest set in the nest, write a deffinition that precisly describs the objects in that set in terms of the objects in the next larger level.
my solution to this qesttion is:
all polygons
Quadrilalateral
tarpezoid
Isosceles Traingle
Rectangle
But i'm not sure about that. Also, i need their deffinitions?

Secondary

Elementary geometry

Post Secondary