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Tanzania [10]
3 years ago
11

Triangle F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the lengt

h of F H is 8. Lines E F and G H are parallel.
What is the length of Line segment G D?

GD =
Mathematics
2 answers:
blsea [12.9K]3 years ago
7 0

Answer:

10.5

Step-by-step explanation:

built different

Ronch [10]3 years ago
3 0

Answer:

10.5

.

.

.

ur welcome ♥️♥️

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Answer:

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Step-by-step explanation:

The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:

\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}

Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).

Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.

\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}

\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}

One can shorten the equation so it only holds the parts that will play a role in solving this equation,

\frac{sin(x)}{10}=\frac{sin(116)}{17}

Now take the cross product in this equation to simplify it further,

\frac{sin(x)}{10}=\frac{sin(116)}{17}

17(sin(x))=10(sin(116))

Inverse operations, solve this equation for (x),

17(sin(x))=10(sin(116))

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x=sin^-^1(\frac{10(sin(116))}{17})

x=31.91782...

x\approx32

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