See below for the proof that the areas of the lune and the isosceles triangle are equal
<h3>How to prove the areas?</h3>
The area of the isosceles triangle is:
Where r represents the radius.
From the figure, we have:
So, the equation becomes
Evaluate
Next, we calculate the length (L) of the chord as follows:
Multiply both sides by r
Multiply by 2
This gives
The area of the semicircle is then calculated as:
This gives
Evaluate the square
Divide
Next, calculate the area of the chord using
Recall that:
Convert to radians
So, we have:
This gives
The area of the lune is then calculated as:
This gives
Expand
Evaluate the difference
Recall that the area of the isosceles triangle is
By comparison, we have:
This means that the areas of the lune and the isosceles triangle are equal
Read more about areas at:
brainly.com/question/27683633
#SPJ1
Answer:
x = 92.5°
Step-by-step explanation:
both are isosceles triangles, with two angles similar
2y + 110 = 180°
2y = 180-110
y = 70/2 = 35°
2z + 65 = 180
2z = 180-65
z = 115/2 = 57.5°
so total angle, x = 35 + 57.5 = 92.5°
In this triangle it is clear that the unknown side x is the hypotenuse of both the triangles that are being formed . So , let us take any one of the triangles and with it's length let us find the length of their hypotenuse which is side x .
= 5² + 5² = x² ( according to the pythagorean theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )
= 25 + 25 = x²
= 50 = x²
= 7.0710678119 = x
But they have given that we have to round it off to the nearest tenths , so ;
= 7.0710678119 will be equal to = 7.10
= 7.1 = x
Therefore , the length of the unknown side x = 7.1 .
Answer:
C. $45
Step-by-step explanation:
Answer:
When you're at the grocery store. For example, you're shopping for paper plates, and the price says they are $4.90, you want to round that to $5 because of tax, and because you don't want to be that person telling the cashier that you don't have enough money.
hope this example is good and helps :)