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Daniel [21]
2 years ago
13

Enlarge the triangle by scale factor 1.5 using (4, 4) as the centre of enlargement.

Mathematics
1 answer:
Goryan [66]2 years ago
3 0
The answer is 6,5 on the graph
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Prove that, in a right triangle with a 15° angle, the altitude to the hypotenuse is one fourth of the hypotenuse.
igomit [66]

Consider the attached figure. If AB has length 1, then BC has length sin(15°) and CD (the altitude of triangle ABC) has length sin(15°)·cos(15°).

By the double angle formula for sin(α), ...

... sin(2α) = 2sin(α)cos(α)

Rearranging, this gives

... sin(α)·cos(α) = sin(2α)/2

We have

... CD = sin(15°)·cos(15°) = sin(2·15°)/2

... CD = sin(30°)/2 = (1/2)/2 = 1/4

That is, the altitude, CD, is 1/4 the hypotenuse, AB, of triangle ABC.

3 0
3 years ago
Can someone help me find the area and perimeter for This and can you explain the process
Eva8 [605]

Answer:

<em>Area of Figure; 3.24π + 21.6 ( square meters ),</em>

<em>Perimeter of Figure; 3.6π + 12 ( meters )</em>

Step-by-step explanation:

As we can see, this picture consists of half circles and a rectangle. If we were to combine each of these half circles, we would get a whole circle with a radius of 1.8 meters;

Area of Circle; πr^2 = π * ( 1.8 )^2 = 3.24π ( square meters ),

If 1.8 is known to be the radius of this full circle, it would be that the diameter is 1.8 * 2 ⇒ 3.6. Knowing that the diameter is one dimension of a rectangle in the picture, we can assume the area of the rectangle to be;

Area of Rectangle; length * width = 6 * 3.6 = 21.6 ( square meters ),

<em>Area of Figure; 3.24π + 21.6 ( square meters )</em>

Now to determine the circumference of these two half circles / whole circle, let us apply the formula 2πr;

Perimeter of Circle; 2πr = 2π * 1.8 = 3.6π

To find the perimeter of the whole figure, we would take the lengths of two of the sides of the rectangles, in addition to the perimeter of the whole circle;

Perimeter of Whole Figure; 3.6π + 6 * 2 = 3.6π + 12 ( meters ),

<em>Perimeter of Whole Figure; 3.6π + 12 ( meters )</em>

3 0
3 years ago
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