"Is the ship in danger of running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 3

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"Is the ship in danger of running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 3

Is there any danger of the ship running aground?

There is a small island A in the sea. There are reefs within 10 nautical miles of the island. Today, a cargo ship sails from west to east. It starts at B, 60° south of island A, and then travels 20 nautical miles east to the south of the island. C at 30° west. After that, the freighter continued to sail eastward.

Do you think there will be a danger of the freighter running aground as it continues sailing east?

To solve this problem, we can mathematicalize it, as shown in the figure:

Analysis: To know whether the freighter is in danger of running aground as it continues to sail eastward, just pass through point A and draw the extension line of AD⊥BC to point D. If AD>10 nautical miles, there is no risk of running aground. According to the meaning of the question, we can see that ∠BAD =60°,

∠CAD=30°,BC= 20 nautical miles.

The problem can be solved by setting AD=x

Mathematical calculations in dams

As shown in the figure, the cross-section of the reservoir dam is trapezoid ABCD, the top of the dam is AD=6m, the slope length is CD=8m. The bottom of the slope is BC=30m, and ∠ADC=135°.

(1) Find the slope of AB;

(2) If the dam is 100m long, how much earth and stone is needed to build the dam (the result is accurate to 0.01m3).

Solution: As shown in the figure, (2) if the dam is 100m long, how much earth and stone is needed to build the dam (the result is accurate to 0.01m3).

From the trapezoidal area formula S=(AD+BC)AF/2, we get,

S=36×4√2/2=72√2

V=100S=100×72√2≈10182.34m3

Answer: A total of approximately 10182.34m3 of earth and stone is required to build this dam.

Summary and aftertaste

What did you gain from this class? What did you learn?

What knowledge was applied?

Use knowledge of trigonometric functions to solve practical problems.

The key is to construct a right triangle.

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"Is the ship in danger of running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 4:

"Is there a danger of the ship running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 4 Knowledge explanation 1. Review the questions and draw pictures. (Reference data: sin55=0.819cos55=0.574tan55=1.428Sin25=0.423cos25=0.906tan25=0.466) The vast sea There is a small...

"Is there a danger of the ship running aground on the rocks?" The relationship between the sides and angles of a right triangle PPT courseware 2:

"Is there a danger of the ship running aground?" The relationship between the sides and angles of a right triangle PPT courseware 2 Review and think about the relationship between the sides and angles of a right triangle The relationship between the three sides of a right triangle: Pythagorean theorem a2+b2=c2. The relationship between the two acute angles of a right triangle: two Acute angles are complementary to each other A+B=90. Three right angles..

"Is the ship in danger of running aground on the rocks?" PPT courseware on the relationship between the sides and angles of a right triangle:

"Is there a danger of the ship running aground on the rocks?" The relationship between the sides of a right triangle PPT courseware Think about it as shown in the figure. There is a small island A in the sea. There are reefs within 10 nautical miles around the island. Today, a cargo ship sails from west to east and starts to go south and west of island A. 55 B, drive east for 20 nautical miles and then reach the south of the island..

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Update Time: 2024-11-10

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