Question

Help me with Highschool Trigonometry pls!

Answer 1

Area of shaded region = (area of big circle - inscribed rectangle) + 2(area of small semicircle - inscribed triangle)

Answer 2

We can work out the dimensions of the inscribed rectangle as well as the small triangles inscribed in the semicircles, by considering half a parallelogram.

The unknown sides are labelled a and b. By Pythagoras Theorem, the oblique side of the parallelogram is sqrt180 cm. Hence algebraic expressions can be derived for each side, in terms of a & b.

Answer 3

We then form simultaneous equations based on Pythaogras Theorem:

\[a^2+b^2=36 -------(1)\]
\[a^2+(\sqrt{180}-b)^2=144 ---------(2)\]

Solve simultaneously to obtain
\[a=\frac{ 12 }{ \sqrt5 }\]
\[b=\frac{ 36 }{ \sqrt{180} }\]

Answer 4

Shaded region =

\[(3.14)(6)^2-(\frac{ 12 }{ \sqrt5 })(\sqrt{180}-\frac{ 36 }{ \sqrt{180} })+2[(\frac{ 1 }{ 2 }(3.14)(3)^2-\frac{ 1 }{ 2 }(\frac{ 12 }{ \sqrt5 })(\frac{ 36 }{ \sqrt{180} })]\]

Answer 5

Answer = 69.3 square centimeters

Answer 6

We can set up the diagram above because all angles in a semicircle are right angles.