The bat fit diagonally across the bottom of the suitcase.
Solution:
Length of the suitcase = 20.5 inches
Width of the suitcase = 29 inches
Using Pythagorean theorem,
Taking square root on both sides, we get
Diagonal of the suitcase = 35.5 inch
Length of the base ball bat = 33 inch
35.5 > 33
Since the diagonal of the suitcase is greater than length of the baseball bat,
The bat fit diagonally across the bottom of the suitcase.
In order to begin we must start off with the formula for the area of a triangle, which is a=1/2b(h) where a is area, b is base, and h is height.
In this scenario, we know that the area is 45cm^2 and the base is 2h+12 (since it is twice it’s height plus twelve). We can plug this into the area equation and then proceed to solve out accordingly.
a=1/2b(h)
45=1/2(2h+12)(h)
90=(2h+12)(h)
90=2h^2 + 12h
0= 2h^2 + 12h - 90
Simplify by dividing the two out.
h^2 + 6h - 45 = 0.
Now plug into the quadratic formula (with a=1, b=6, and c=-45) as shown in the image below.
After plugging the equation in and solving, we come to the idea that h is roughly equal to 4.34. We can now plug this back into the triangle area formula to solve out for b.
a=1/2b(h)
45=1/2(2h + 12)(h)
45=1/2(20.69)(4.34)
45=45.
In conclusion;
The height is ≈ 4.34
The base is ≈ 8.68
Hope this helps :)
Here's the solution ~
Let's find the measure of hypotenuse first, by using Pythagoras theorem ;
Now, let's find the asked values ~
For Cos y :
As we can see that both sin x and Cos y have equal values, therefore The required relationships is equality.
I.e Sin x = Cos y
Hope it helps ~
