A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.

According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.

The remaining angle of the rhombus will be calculated as thus;

= 360° - (32°+32°)

= 360° - 64°

= 296°

This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°

This means that each obtuse angles of the rhombus will be 148°.

To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.

m° = 148°/2

m° = 74°

Hence the angle measure if m(1) is 74°

4 0

3 years ago

5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.

lesya692 [45]

9514 1404 393

Answer:

±√58 ≈ ±7.616

Step-by-step explanation:

The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.

|x| = √(3² +7²) = √58

The motion is bounded between positions ±√58.

_____

Here's a way to get to the relation used above.

The sine of the sum of angles is given by ...

sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)

If this is multiplied by some amplitude A, then we have ...

A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)

Comparing this to the given expression, we find ...

A·cos(c) = 3 and A·sin(c) = -7

We know that sin²+cos² = 1, so the sum of the squares of these values is ...

(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²

That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...

x = A·sin(θ +c) . . . . for some angle c

x = (√58)sin(θ +c)

This has the bounds ±√58.

3 0

3 years ago