A, B & C form a triangle where Z BAC = 90°. AB = 7.3 mm and CA = 4.6 mm.
Find the length of BC, giving your answer rounded to 1 DP.

BC ≈ 8.6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle , that is

BC² = AB² + AC² = 7.3² + 4.6² = 53.29 + 21.16 = 74.45 ( square root both sides )

BC = ≈ 8.6 ( to 1 dec. place )

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

is there a question here?

step-by-step explanation: