Question

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?

Answer 1

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.

$\frac{12}{8}=\frac{8}{x}$

$x=\frac{8\times 8}{12}=\frac{64}{12}=5.3 ft$

$x=\frac{64}{12}\times 12=64 inches$=5 ft 4in

1 feet=12 inches

(2)In triangle DBC

$CD^2=BC^2+DB^2$

Using Pythagoras theorem  

$(hypotenuse)^2=(Base)^2+(perpendicular\;side)^2$

$CD^2=(8)^2+(5.3)^2$

$CD=\sqrt{64+28.09)}=9.6 feet$

Hence, the length of support wire=9.6 feet