You have two 30-60-90 triangles, ADC and BDC.
The ratio of the lengths of the sides of a 30-60-90 triangle is
short leg : long leg : hypotenuse
1 : sqrt(3) : 2
Using triangle ADC, we can find length AC.
Using triangle BDC, we can find length BC.
Then AB = AC - BC
First, we find length AC.
Look at triangle ACD.
DC is the short leg opposite the 30-deg angle.
DC = 10sqrt(3)
AC = sqrt(3) * 10sqrt(3) = 3 * 10 = 30
Now, we find length BC.
Look at triangle BCD.
For triangle BCD, the long leg is DC and the short leg is BC.
BC = 10sqrt(3)/sqrt(3) = 10
AB = AC - BC = 30 - 10 = 20
Answer: cos(53o)=y/5
<span>T
riangle abc is a right triangle and sin(53o) = . solve for x and round to the nearest whole number. which equation correctly uses the value of x to represent the cosine of angle a?cos(53o) = 4/xcos(53o) = y/5cos(53o) = x/4cos(53o) = 5/y</span>
Answer:
All together Dino has 2 dollars and 14 cents.
Step-by-step explanation:
I hope this helps. Sorry if I am wrong.
Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have
We can expression one variable in terms of the others as
Since the area is the product of the dimensions, we have
This is a parabola facing down, so it's vertex is the maximum:
So, the maximum is
And since we know that 
, we have 
as well.
This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.
