Question

Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles, QRP and ARC, as shown in the figure below. The length of segment PR is 1.8 inches and the length of segment CR is 3.3 inches. The distance between A and C is 6.6 inches.
(Image being added shortly)

What is the distance between the endpoints of the beams P and Q?

a.) 0.9 inches
b.) 1.8 inches
c.) 2.5 inches
d.) 3.6 inches

Answer 1

cos theta=pq/1.8
cos 45=pq/1.8
pq=1.8 cos 45

Answer 2

pqr is forming right triangle

Answer 3

thank you