Calculate the area of an isosceles right triangle who's hypotenuse is 42–√ inches.

A =    441  in²  

Step-by-step explanation:

An isosceles right triangle is a triangle with two equals sides (the legs ). In this particular case the base of the triangle will be the length of one side and at the same time the height of the triangle will be the other leg.  Hypotenuse as always is the opposite side to the right angle.

The area of a triangle is

A =  (1/2) * b* h

If we are going to compute the area of such triangle we have to find the length of one side That will be the base of the triangle and at the same time that will be the height of the triangle.

In any right triangle  hypotenuse is:

H²  = L₁²  +  L₂²    (1)

As was explain before  in this particular case  L₁  = L₂

Then

H²  =  L₁² +  L₁²    ⇒    H²  =  2 L₁²        H  =  √2 * L₁      ⇒   L₁  =  42/√2  

Then area of the  

A = (1/2)* ( 42/√2) *   ( 42/√2 )    ⇒     A = 1/4 * (42)²  

A =    441  in²    

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step-by-step explanation:

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9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841