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2 years ago

3d trigenomatry , need help , with step by step working please

Mathematics

1 answer:

Law Incorporation [45]2 years ago

4 0

The angle you want - call it θ - is such that

tan(θ) = FC / AC

Find the length of the diagonal AC, i.e. a diagonal of the rectangle ABCD. ABC forms a right triangle with legs AB = 70 and BC = 50, so

AC² = AB² + BC²

→ AC = √(70² + 50²) = 10 √74

Find FC using the given angle of the sloping face:

tan(30º) = FC / BC

→ 1/√3 = FC / 50

→ FC = 50/√3

Now solve for θ :

tan(θ) = (50/√3) / (10 √74)

→ tan(θ) = 5/√222

→ θ ≈ 18.6º

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3 years ago

Triangles are similar. Round answer to nearest tenth (step by step)

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2 years ago

Read 2 more answers

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago