Mathematics, 30.07.2019 13:30 sebasp42

In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. find the measures of the angles of the rhombus.

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The obtuse angles will measure 120° and the acute angles will measure 60°.

Drawing the altitude forms a right triangle. Let the side of the rhombus be x. The altitude bisects the opposite side, so the base of the triangle formed would be 1/2x. We have an expression for the side opposite this portion of the obtuse angle (cut by the altitude) and for the hypotenuse (the side length of the rhombus, x). opposite/hypotenuse is the ratio for sine. Our equation then looks like this:
$\sin x=\frac{\frac{1}{2}x}{x} 
\\ \sin x=\frac{1}{2}x \div x
\\ \sin x=\frac{1}{2}x \div \frac{x}{1}
\\ \sin x=\frac{1x}{2} * \frac{1}{x}=\frac{1x}{2x}=\frac{1}{2}$
Now we take the inverse sine of both sides:
sin⁻¹(sin x)=sin⁻¹(1/2)
x=30

Since this portion of the triangle is 30, and the right angle is 90, the missing angle (an acute angle of the rhombus) is 180-30-90=60°. Since the acute angles and obtuse angles of a rhombus are supplementary, the obtuse angles must be 180-60=120°.

Answer from: chels8547

The angles of the rhombus determines the inclination of the sides of the

rhombus.

The correct response;The measures of the four angles of the rhombus are 60°, 60°, 120°, and 120°.Method used to arrive at the above response;Given;

The altitude of the rhombus bisects the opposite side.

The angle of the rhombus at the vertex point of the altitude = An obtuse angle

Required:

The measure of the angles of the rhombus

Solution:

The length of the sides of a rhombus are equal.

The opposite angles of a rhombus are equal.

Let x represent the length of a side of the rhombus, we have;

The bisector from the vertex of the obtuse angle = An altitude

The angle the altitude forms with the side it bisects = 90°

Therefore;

The triangle formed by the altitude, half the bisected side and the side of the rhombus adjacent to the bisected side = A right triangle

The hypotenuse side to the right triangle = The side of the rhombus

Let θ represent the angle opposite the altitude, and between the sides of

the rhombus, in the right triangle by trigonometric ratios, we have;

$\displaystyle cos(\theta) = \mathbf{\frac{Adjacent}{Hypotenuse}}$

$\displaystyle cos(\theta) = \frac{0.5 \cdot x}{x} = 0.5$

θ = arccos(0.5) = 60°

Therefore, two acute (opposite) angles of the rhombus are 60°

The two obtuse angles of the rhombus are each = (360° - 2×60°) ÷ 2 = 120°

The angles of the rhombus are 60°, 60°, 120°, 120°.

Learn more about trigonometric ratios here:

link

In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. find the mea

Answer from: Quest

4should be the last one n=4

Answer from: Quest

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²

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In a rhombus, an altitude from the vertex of an obtuse angle bisects the opposite side. find the mea...

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