Apply the 30-60-90 triangle theorem to find the length of the longer leg of a triangle of the length of the shorter leg is 4 inches. 3square root 4
7 inches
4 square root 2
8 square root 3

4sqrt(3) inches

Step-by-step explanation:

The ratio of the lengths of the legs of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

1 : sqrt(3) : 2

The long leg is sqrt(3) times the length of the short leg.

Here, the short leg measures 4 inches.

long leg = sqrt(3) * short leg

long leg = 4sqrt(3) inches

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

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