For a right triangle the length of the two sides a and b can be squared and added together to get the length of the hypotenuse c. So a^2 b^2 = c^2. Since this a sector of a circle we know that the length of OB = OA. So 26^2 26^2 = c^2 which in this instance is the length of AB. So 676 676 = 1352 and the square root of which is 36.8. Now half of that is the length of CB which is 18.4. 18.4^2 (OC)^2 = 676, or 338.6 (OC)^2 = 676. Subtracting 338.6 from both sides gives you (OC)^2 = 337.4 and the square root of which is 18.4. The area of a triangle is 1/2 × height × width so for triangle OAB the area equals 1/2 × 36.8 × 18.4; or 338.6. Now the area of a circle is pi × R^2 or 676pi or 2123.7. And the sector represents 82/360 of the area of the circle. Which 2123.7 × 82/360 = 483.7. So the percentage of the shaded area of the diagram is 338.6 ÷ 483.7 × 100 which equals 70%. All the numbers I used were rounded to the nearest tenth. And hopefully G@G doesn't convert anything into an emoji.
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OC=26 cos41degree
BC= 26 sin 41 degree
area of OAB= OC*BC
area of sector=153.45π percentage shaded= area of OAB/total area *100
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