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vladimir2022 [97]

3 years ago

13

The angle of elevation to the sun is 24°. What is the length of the shadow cast by a person 1.82 m tall? A. 0.81 m B. 1.99 m C.

4.09 m D. 4.47 m

1 answer:

Zanzabum3 years ago

7 0

Answer:

C. 4.09 m

Step-by-step explanation:

Let the length of the shadow cast by a person be x m.

$\tan \: 24 \degree = \frac{height \: of \: person}{length \: of \: the \: shadow} \\ \\ 0.4452286853 = \frac{1.82}{x} \\ \\ x = \frac{1.82}{0.4452286853} \\ \\ x = 4.08778693 \: m \\ x = 4.09 \: m$

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Answer:

See below

Step-by-step explanation:

1)

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2)

$\frac{12x + 11}{x^2 +x - 6}$

$=\frac{12x + 11}{x^2 +3x-2x - 6}$

$=\frac{12x + 11}{x(x +3) -2(x +3)}$

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}$

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}$

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}$

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Equating like terms on both sides:

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$- 2A + 3B = 11... (2)$

Solving equations (1) & (2), we find:

A = 5, B = 7

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}$

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