Find the length of down tube and angle between seat tube and down tube

Question

The following problem refers to the figure below, which is a diagram of a bike frame. The frame can be approximated as two triangles that have the seat tube as a common side.

Suppose the frame has a top tube length of 53.2 centimeters, a seat tube length of 47.0 centimeters, and a seat angle of 80.0°. Find the length of the down tube and the angle between the seat tube and the down tube. (Round your answers to one decimal place.)

length of down tube	______cm
angle between seat tube and down tube	_______°

Answer 1

Use Law of Cosines

d² = 53.2² + 47.0² - 2(53.2)(47.0) cos 80°

Use down tube length and Law of Sines toe determine angle between down tube and seat tube.