Mathematics, 09.12.2019 16:31 sabrinamarie391

Which set of values could be the side lengths of a 30-60-90 triangle?

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Answer from: 1846252

If we say that side "a" is the shortest (adjacent), side "b" is the second shortest (opposite), and side "c" is the longest (hypotenuse): then angle A would be 30°, angle B would be 60°, and angle C would be 90°

tan B = b/a
or
a tan B = b

they have 4 as the smallest value in all four options, so we know that a=4

4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3

that leaves two options left, so now we find "c":

c^2 = (a^2) + (b^2)
OR
$c= \sqrt{a^{2} + b^{2}}$

$c= \sqrt{4^{2}+(4\sqrt{3})^{2}}$

$c= \sqrt{16+48} \\ c=\sqrt{64} \\ c=8$

so a=4, b=4√3, and c=8

Making your answer B

Answer from: hjgjlgkjg

A triangle with 30°, 60° & 90° angles is called a semi equilateral triangle.

In such a triangle the hypotenuse equal the side of the equilateral triangle, and the opposite side to the angle 30° is equal half the side of the equilateral or half the hypotenuse.

Assume the side equal 8 & the other 8/2 = 4. let's calculate the 3rd side by applying Pythagoras:

8² = 4² + x² ; 64 = 16 + x² or x² = 64-16 ; x² =48 and
x =√48 = √16. 3 = 4√3

So the 3 sides are 8, 4 and 4√3 (answer B)

Answer from: Quest

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

Which product is shown on this number line

Answer from: Quest

solution:

the given function is ,

$f(x) = 4 x^3 - 72 x^2 + 320 x,$

= $4x( x^2- 18 x + 80)\\\\ 4 x(x^2-10 x -8 x + 80) \\\\ 4 x[(x-10)(x-8)]$

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

$f(x) = a x^3+ b x^2 + c x+d,$

sum of the roots = a + b +c= 0+8+10=18= $\frac{-b}{a}$

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 = $\frac{c}{a}$

product of roots = a b c = 0= $\frac{d}{a}$

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function $f(x) = 4 x^3 - 72 x^2 + 320 x,$ is given by entry and exit route of this hall.

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