For the angles α and β in the figures, find cos(α + β)?

Mathematics

2 answers:

Svet_ta [12.7K]2 months ago

4 0

For the small triangle, both legs are known, allowing the use of the tangent function to determine the angle. In the larger triangle, we know the hypotenuse and the opposite leg, which enables the use of the sine function for angle calculation. Thus, the total of these angles will lead us to the solution.

Inessa [12.5K]2 months ago

3 0

Let h units denote the hypotenuse of the smaller triangle. From the Pythagorean Theorem, we derive specific relationships involving the smaller triangle with dimensions

$\cos (\alpha)=\frac{4}{2\sqrt{5} }=\frac{2}{\sqrt{5} }$ along with the shorter leg of the second triangle denoted as s units. Furthermore, we apply the double angle property and substitute values to arrive at the final calculation.

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Solve the following problem: An investor earned triple the profits of what she earned last year. If she made $500,000.48 total f

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Response:

$125,000.12 last year

$375,000.36 this year

Step-by-step clarification:

Last year, her earnings were x.

This year, her earnings are three times greater, thus they equal 3x.

For both years combined, the total earnings amount to x + 3x = 4x.

The earnings across both years together total $500,000.48

4x = 500,000.48

Dividing both sides by 4 gives us

x = 500,000.48/4

x = 125,000.12

Thus, last year's earnings were $125,000.12

This year, her profits amounted to 3x = 3(125,000.12) = 375,000.36, totaling $375,000.36

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