Finding angle in triangle and semicircle

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Homework Help Overview

The discussion revolves around a geometry problem involving a semicircle and an isosceles triangle that share the same base and area. The goal is to find the angle x in the triangle, with the context being part of a coursebook for IGCSE mathematics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are exploring the relationship between the areas of the semicircle and the triangle, questioning how to express the area of the triangle given that it is not directly provided. There is a suggestion to split the triangle into right-angled triangles to facilitate calculations.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the problem setup and explore potential methods for calculating the area of the triangle. Some guidance has been offered regarding the areas, but no consensus or resolution has been reached yet.

Contextual Notes

Participants note that the areas of both shapes are equal, but specific values are not provided, leading to uncertainty in calculations. The problem is framed within the constraints of IGCSE homework guidelines.

jacky50
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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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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:
 


Hey tiny-tim, thanks :)

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

I'm asking you what they are
 


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

Split it into two right-angled triangles.
 

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