Question

A door with width 4.20m has an arc as shown in the diagram. Find: a) the radius of the arc, to the nearest cm. b) the length of the arc, to the nearest cm

Answer 1

a. 2m

b. 5m

Explanation:

a. from the triangle assuming ABC

half triangle ABC will be ABO and ACO

AO = OB = 4.20m ÷ 2

AO = OB = 2.1m

finding the angle between AB and AC

360 - 225 = 135°

the angle between AB and AO

135÷2= 67.5°

using sin to find the length of AB = radius

sin 67.5 = 2.1/r

r= 2.2730 ~2m

b. theta/360 ×2πr = length of the arc

L= 135/360×2×22/7 × 2.2730

Length of the arc = 5.3578m ~ 5m

Answer 2

Hi there!

~

`R = (2.1)/(sin 67.5)`

`Arc = R`
`(3\pi )/(4)`

(A)

Hope this helped you!