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3 years ago

Find all solutions of the equation. 5 sin x − 82√ = 3 sin x − 72√

Mathematics

1 answer:

Andrei [34K]3 years ago

6 0

Answer:

x = arcsin(√20.5 -3√2) +2kπ . . . k any integer
x = π - arcsin(√20.5 -3√2) +2kπ . . . k any integer

Step-by-step explanation:

Add √(82) -3sin(x) to both sides to get ...

2sin(x) = √82 -√72

Now, divide by 2 and find the arcsine:

sin(x) = (√82 -√72)/2

x = arcsin((√82 -√72)/2)

Of course, the supplement of this angle is also a solution, along with all the aliases of these angles.

___

In degrees, the solutions are approximately 16.562° and 163.438° and integer multiples of 360° added to these.

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to estimate the height of the jin mao tower in shanghai , a tourist sights the top of the tower form a mirror that is 86.7 meter

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The height of the tower = 420.48 meters

Step-by-step explanation:

For better understanding of the solution, see the figure attached below :

Let the height of the tower be x meters

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Similarly, ∠D = ∠r ( Alternate interior angles)

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⇒ ∠A = ∠D

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∠A = ∠D (Proved above)

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So, by AA postulate of similarity of triangles, ΔABC ~ ΔDEC

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$\frac{AB}{DE}=\frac{BC}{EC}\\\\\implies\frac{1.92}{x}=\frac{0.4}{87.6}\\\\\implies x=\frac{87.6\times 1.92}{0.4}\\\\\bf\implies x = 420.48\textbf{ meters}$

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