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The drawing below represents the frame for an isosceles triangle-shaped roof. The height of the roof is 4 feet. What is the distance from Point A to Point B in feet? B 41 3 feet 8v 6 feet 8V3 feet 8 feet

The Drawing Below Represents The Frame For An Isosceles Triangleshaped Roof The Height Of The Roof Is 4 Feet What Is The Distance From Point A To Point B In Fee class=

Sagot :

We can make a drawing to see better:

In the picture above, we can see the sides AC and BC are equals because triangle ABC is isosceles, and also the segments AD and DB are equals for the same reason.

We can calculate the lenght of segment AD as:

[tex]\begin{gathered} \tan (30)=\frac{CD}{AD} \\ AD=\frac{CD}{\tan (30)}=\frac{4}{\frac{1}{\sqrt[]{3}}} \\ AD=4\cdot\sqrt[]{3} \end{gathered}[/tex]

With the lenght of segment AD we can calculate the lenght of AB as:

[tex]AB=2\cdot AD=8\cdot\sqrt[]{3}[/tex]

The correct answer is in yellow.

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