I need help with trigonometry

Mathematics

1 answer:

MrMuchimi2 years ago

6 0

Answer:

In alphabetic order:

x can be found with pythagorean theorem, since triangle ADC is right in D.

$x= \sqrt {7^2-2.2^2} \approx 6.6$

y and z are 7 times respectively the sine and cosine of angle ACB.

$y= 7sin\ 52\° \approx 5.5\\z=7 cos\ 52\° \approx 4.3$

Finally, $\theta$ can be calculated by determining the arc sine (or inverse sine) of the ratio CD over AC

$\theta = sin^{-1} (\frac{2.2}7) \approx 18.3\°$

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The base of a parallelogram is 10 units and the height is 7units. A segment divides the parallelogram into two identical trapezo

sveticcg [70]

If you need area of the trapezoids:

Area of parallelogram = 10×7 = 70 sq. units

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8 0

3 years ago

What is the volume of this cone?

olchik [2.2K]

Answer:

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

$a^2 = b^2 + c^2$

So we can find the height of the cone with that:

$10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx 7.9$

Now that we have the cone's height, we can solve for its volume:

$v = \frac{1}{3} \pi r^2 h\\v = \frac{1}{3} \pi \times 7.4^2 \times 7.9\\v = \frac{1}{3} \pi \times 54.76 \times 7.9\\v = \frac{1}{3} \pi \times 432.6\\v = \pi \times 144.2\\v \approx 453.0 cm^3$