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wariber [46]
3 years ago
14

Solve for x. Round to the nearest hundredth.

Mathematics
1 answer:
Airida [17]3 years ago
3 0

Answer: 32.98^{\circ}

Step-by-step explanation:

Since, By the given diagram,

In quadrilateral ABCD, all angles are right angles ⇒ DC = AB = 15 cm and CB = DA

Also, In triangle DFA,

sin 56^{\circ} = \frac{DA}{DF}

⇒ sin 56^{\circ} = \frac{DA}{16}

⇒ 16\times sin 56^{\circ}=DA

⇒ 13.2646011609\text{ cm} = DA

Now, In triangle, DEC,

tan x = \frac{EC}{DC}

⇒ tan x = \frac{EB-CB}{DC}

⇒ tan x = \frac{EB-DA}{DC}

⇒ tan x = \frac{23-13.2646011609}{15}  

⇒ tanx = \frac{9.73539883912}{15}

⇒ tanx = 0.64902658927

⇒ x = 32.9846428556^{\circ} \approx 32.98^{\circ}



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Answer:

Area of the shaded part is 3.14 square unit.

Step-by-step explanation:

Area of the shaded part = Area of large semicircle - (Area of two small semi circles)

Area of large semicircle with center O = \frac{1}{2}(\pi r^2)

                                                                = \frac{1}{2}\pi (2)^{2}

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Area of semicircle with center O' = \frac{1}{2}\pi (1)^2

                                                      = \frac{\pi }{2}

Area of semicircle with center O" = \frac{\pi }{2}

Now substitute these values in the formula,

Area of shaded part = 2\pi - (\frac{\pi }{2}+\frac{\pi }{2})

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Area of the shaded part is 3.14 square unit.

7 0
2 years ago
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Please help me solve
mihalych1998 [28]

Answer:

x = 36.3°

using tane rule:

\sf tan(x)= \dfrac{opposite}{adjacent}

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=============

\hookrightarrow \sf tan(x) = \dfrac{22}{30}

\hookrightarrow \sf x= tan^{-1}(\dfrac{22}{30} )

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