The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.
<h3>What is a Rhombus?</h3>
A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.
<h3>What is the above proof?</h3>
- ∠DEC ≅ ∠BFC Reason = All Right Angles with Equal dimensions are congruent.
- ∠C ≅ ∠C Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.
- Δ DEC ≅ Δ BFC Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
≅
Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.- ABCD is a Rhombus Reason = Its sides are all congruent.
Learn more about Rhombus at;
brainly.com/question/20627264
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Dakota runs every 6 weeks......so he runs at 6 weeks, 12 weeks, 18 weeks, 24 weeks, 30 weeks
Madison runs every 15 weeks...so she runs at 15 weeks, 30 weeks, 45 weeks
so they will both be running a half-marathon at 30 weeks <==
Answer:
The length of the longer leg is ![7\sqrt{3}\ units](https://tex.z-dn.net/?f=7%5Csqrt%7B3%7D%5C%20units)
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In any triangle:
The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle
so
The longer leg is AC
we have
----> by SOH (opposite side divided by the hypotenuse)
Remember that
![sin(60^o)=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=sin%2860%5Eo%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
![AB=14\ units](https://tex.z-dn.net/?f=AB%3D14%5C%20units)
substitute the given values
![\frac{\sqrt{3}}{2}=\frac{AC}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%3D%5Cfrac%7BAC%7D%7B14%7D)
![AC=7\sqrt{3}\ units](https://tex.z-dn.net/?f=AC%3D7%5Csqrt%7B3%7D%5C%20units)