Circle Geometry Math Problem Help? (diagram attached)?
A man designs a garden as shown. From point D outside the circle with centre C, two tangents, DA and DB, each 12 ft in length, meet the radius of the circle at points A and B respectively. Determine the total area of the man's garden.
- Mike GLv 76 months agoFavorite Answer
tan θ = 12/5
2θ = 134.76°
Central Reflex Angle = 360-134.76 = 225.24°
= 225.24π/180 radians
Area of circular part = 0.5*25*225.24π/180
= 49.14 ft^2
Area of the two triangles = 60 ft^2
Total Area = 109.14 ft^2
- PuzzlingLv 76 months ago
The area of the two triangle sections is easy to figure out. They are right triangles, so they each have an area of ½(5*12) = 30 ft² for a total of 60 ft².
So we just need the larger sector ACB.
Start by figuring out the angle θ using trigonometry:
tan θ = 12/5
θ = arctan(12/5)
θ = 67.38°
That means the central angle for the outside sector ACB is:
360° - 2θ
≈ 360° - 2 * 67.38°
Now just take the full circle (π5² = 25π sq. ft.) and take the fraction for the sector.
Asector = (225.24 / 360) * 25π
Asector ≈ 39 sq. ft.
Add the 60 sq. ft. we previously calculated for the triangles.
~99 sq. ft.
- Anonymous6 months ago
Do it yourself. We're not gonna do your fuсking homework for you.