Question

Here’s a picture of a bicycle frame. The seat angle is the angle formed by the top tube and seat tube. If the top tube measures 56.9 cm, the seat tube is 57 cm, and the down tube is 67.8 cm, find the seat angle. Round answer to the nearest degree.

Head tube Top tube -Seat stays Seat tube Down tube Bottom bracket Chain stays Drop outs

Answer 1

Consider the picture for reference.

We want to find the angle BAC. Let it be equal to A.

569 cm B B A 57 cm 67.8-0m e C

According to law of Cosines,

$a^{2}$ = $b^{2}$ + $c^{2}$ - 2bc CosA

In this figure,

a = 67.8 cm , b = 57 cm , c = 56.9 cm

[ Here a is the side opposite to the angle A, b is the side opposite to the angle B and c is the side opposite to the angle C]

Putting these values, we get

4596.84 = 3249 + 3237.61 - 6486.6 CosA

》 CosA = 0.29133

A = $cos^{-1}$ (0.29133)

A = 73.06°