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

Hi there!

~

$R = \frac{2.1}{sin 67.5}$

$Arc = R$ $\frac{3\pi }{4}$

(A)

Hope this helped you!

Answer 2

Answer:

a. 2m

b. 5m

Step-by-step 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