Answer:
x = 8*root3
y = 16
Step-by-step explanation:
You can use tangent and cosine of 60° to find x and y, BUT THERE'S A SHORTCUT. You pointed out that its a 30°-60°-90° triangle. That is a special right triangle. Here's the shortcut:
the longest side (hypotenuse) is double the shortest side. We have an 8 on the shortest side, so the hypotenuse (longest side) is 16. This ALWAYS works for 30°-60°-90° triangles!
Another shortcut:
The longer leg is the shorter leg × root3.
This ALWAYS works on 30°-60°-90° triangles.
So on your triangle, the short side is 8, that means the longer leg is 8×root3.
ta-daaaa!
Answer:
68
Step-by-step explanation:
Let x=adult tickets and y=child tickets
1) 15x+11y=1889
2) x+y=147
multiply equation 1 by -1/11 on both sides to get:
-(15/11)x-y=-171.73
add new equation with equation 2 to get
-4/11x=-24.73
Isolate x to get:
x=67.99999
Round up to get 68 adult tickets
If Sally already has 3 marbles and she finds 5 everyday. That means you add 5 until you get to 58. So in this case 5 times 11 is 55 + 3 is 58. Answer: It will take 11 days at this rate for her to have 58 marbles.
Answer
Find out the length of the shorter and longer pieces of a board .
To prove
Let us assume that the length of the shorter pieces be x.
As given
Jared has a wooden board that is 11 ft long.
He wants to cut it into two pieces so that the longer piece is 4 ft less than 4 times the length of the shorter piece.
Than the length of the longer pieces = 4x - 4
Than the equation becomes
x + 4x - 4 = 11
5x = 11 + 4
5x = 15

x = 3 ft
Therefore the length of the shorter pieces be 3 ft .
The length of the longer pieces = 4x - 4
= 4 × 3 - 4
= 12 - 4
= 8 ft
Therefore the length of the longer pieces be 8 ft .