Answer. and you!
there's a picture of the question, but i'll write it out so it's clearer.
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.
(the questions are on the image)
if someone with smarts in geometry could answer, that'd be appreciated.

(a) BD = 5 ft 4 in.

(b) CD = 9.6 ft

Step-by-step explanation:

You need to look carefully at what you have to figure out what strategy to use to solve the problem. Notice that triangle ACD is a right triangle. Segment CB is an altitude of triangle ACD drawn from vertex D to side AD. CB is perpendicular to AD. That makes triangles ACB and DCB right triangles. In other words, you have three right triangles. Now look at this theorem:

The Right Triangle Altitude Theorem

If an altitude is drawn in a right triangle, then the two triangles formed and the original triangle are similar triangles.

We are dealing with similar triangles ABC, CBD, ACD.

The lengths of corresponding sides of similar triangles are proportional.

(a)

AB/BC = BC/BD

12/8 = (8 ft)/BD

12(BD) = 64 ft

BD = 64/12 ft

BD = 16/3 ft

BD = 5 1/3 ft

BD = 5 ft 4 in.

(b)

The support wire is side CD in right triangle BCD. Side CD is the hypotenuse of right triangle BCD. We know the lengths of the two legs, so we can use the Pythagorean theorem to find the length of the hypotenuse.

(BC)^2 + (BD)^2 = (CD)^2

(8 ft)^2 + (16/3 ft)^2 = (CD)^2

64 ft^2 + 256/9 ft^2 = (CD)^2

576/9 ft^2 + 256/9 ft^2 = (CD)^2

832/9 ft^2 = (CD)^2

CD = 9.6 ft