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A wooden structure has the shape of a right triangle with a base of 12 feet and a height of 8 feet. It is supported by a wire stretched from point C to the ground at point D such that the support wire is perpendicular to the top of the structure, AC.


(1) how far away from point b should point d be placed? give an exact answer in feet and inches.

(2) to the nearest tenth of a foot what is the length of the support wire?

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lublana

Answer:

(1)5 ft 4 in

(2)9.6 ft

Step-by-step explanation:

We are given that

AB=12 ft

BC=8 ft

All right triangles are similar

(1)Let BD=x

Triangle ABC and DBC are similar

When two triangle are similar then , the ratio of their corresponding sides are equal.

[tex]\frac{12}{8}=\frac{8}{x}[/tex]

[tex]x=\frac{8\times 8}{12}=\frac{64}{12}=5.3 ft[/tex]

[tex]x=\frac{64}{12}\times 12=64 inches[/tex]=5 ft 4in

1 feet=12 inches

(2)In triangle DBC

[tex]CD^2=BC^2+DB^2[/tex]

Using Pythagoras theorem  

[tex](hypotenuse)^2=(Base)^2+(perpendicular\;side)^2[/tex]

[tex]CD^2=(8)^2+(5.3)^2[/tex]

[tex]CD=\sqrt{64+28.09)}=9.6 feet[/tex]

Hence, the length of support wire=9.6 feet

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The distance from point B that point D should be placed in the triangle is 5 feet 4 inches.

How to solve the triangle?

The distance from point B that point D should be placed in the triangle will be calculated thus:

Let the distance be represented by x

12/8 = 8/x

x = (8 × 8) / 12

x = 5 ft 4 in

The length of the support wire will be calculated thus:

CD² = 8² + 5.3²

CD² = 64 + 28.09

CD² = 92.09

CD = ✓92.09

CD = 9.6 feet

Therefore, the length of the support wire is 9.6 feet.

Learn more about triangles on:

https://brainly.com/question/17335144

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