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sladkih [1.3K]
3 years ago
9

If segment FD = 20 units and segment DE = 52 units, what is the value of b? Round the solution to the nearest hundredth.

Mathematics
1 answer:
Readme [11.4K]3 years ago
7 0

Answer:

b = 22.62^{o}

Step-by-step explanation:

Since the triangle is a right angled triangle, the appropriate trigonometric function can be applied to determine the value of b.

Thus, to determine the value of b;

Sin θ = \frac{opposite}{hypotenuse}

Sin b =  \frac{20}{52}

         =  \frac{20}{52}

          = 0.38462

⇒ b = Sin^{-1} 0.38462

  = 22.6202

b = 22.62^{o}

The measure of angle E (= b) is 22.62^{o}.

         =

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The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:

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The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.

The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.

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For our triangle, the base is b=4in and the height is h=6in, then the area is:

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