Finding angle in triangle and semicircle

In summary, the conversation is about a question regarding the calculation of an angle in a semi-circle and an isosceles triangle with the same base and area. The solution involves splitting the triangle into two right-angled triangles and using the formula for the area of a semi-circle. The final answer is 57.5°.
  • #1
jacky50
3
0
Dear all,
right now, I am doing my IGCSE and this question is in my coursebook. I can't think of any way to calculate it...
It's part of the section circumference and area of circles. So must be some how solved using this.

The semi-circle and the isosceles triangle have the same base AB and the same area. Find the angle x.
The answer is: 57.5°

Thanks a lot in advance
Jacky
 

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  • #2
Welcome to PF!

Hi Jacky! Welcome to PF! :wink:

Call the angle x, and the length AB 1 …

what are the areas of the triangle and the circle? :smile:
 
  • #3


Hey tiny-tim, thanks :)

the area is not given, just that its the same
 
  • #4
I know they're not given …

I'm asking you what they are
 
  • #5


Area of semi-circle = 0.5 x pi x (0.5AB)^2
But I don't have a clue about the triangle
 
  • #6
jacky50 said:
But I don't have a clue about the triangle

Split it into two right-angled triangles.
 

FAQ: Finding angle in triangle and semicircle

How do you find the angle of a triangle using the Pythagorean Theorem?

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse. To find the angle of a triangle using this theorem, you would first identify the two shorter sides and the hypotenuse. Then, you would use the formula c² = a² + b², where c represents the length of the hypotenuse and a and b represent the lengths of the other two sides. Finally, you would take the square root of both sides to solve for c, which would give you the length of the hypotenuse. From there, you can use inverse trigonometric functions to find the angle.

How do you find the angle of a triangle using the Law of Sines?

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. To find the angle of a triangle using this law, you would first identify the length of two sides and the measure of the angle opposite one of those sides. Then, you would set up the equation a/sinA = b/sinB, where a and b represent the lengths of the two sides and A and B represent the measures of the opposite angles. You can then solve for the unknown angle by taking the inverse sine of both sides of the equation.

How do you find the angle of a triangle using the Law of Cosines?

The Law of Cosines states that the square of the length of a side of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. To find the angle of a triangle using this law, you would first identify the lengths of all three sides. Then, you would use the formula c² = a² + b² - 2abcosC, where c represents the length of the side opposite the angle you are trying to find and a and b represent the lengths of the other two sides. You can then solve for the unknown angle by taking the inverse cosine of both sides of the equation.

How do you find the angle of a semicircle?

The angle of a semicircle is always 180 degrees, or π radians. This is because a semicircle is half of a circle, and the total angle of a circle is 360 degrees, or 2π radians. Therefore, to find the angle of a semicircle, you can simply divide 360 degrees or 2π radians by 2.

How do you find the angle of a triangle if all three side lengths are known?

If you know the lengths of all three sides of a triangle, you can use the Law of Cosines to find the measure of any angle. First, you would use the formula c² = a² + b² - 2abcosC to solve for the angle measure. Then, you would take the inverse cosine of both sides of the equation to find the angle measure in degrees or radians. Alternatively, you can also use the Law of Cosines to find the angle opposite the known side by setting up the equation cosC = (a² + b² - c²)/(2ab) and taking the inverse cosine of both sides.

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