In △abc, m∠cab=30° and m is the midpoint of ab so that ab=2cm. find the angles of the triangle. find ab if bc=7 ft.

angle ACB = 90 degrees

angle B  = 60 degrees

AB = 14ft.

hypotenuse side AB is twice than BC, i.e. 14 ft.

Step-by-step explanation:

Given data:

angle CAB =  30 degree

M is mid point of AB  and AB = 2 times of CM

We can say that, |MA| = |MB| = |MC|.  and point A, B, and C are equidistant from M.  It signifies that the point M is act as center of the circle which circumscribed around the  given triangle ABC.  

Therefore AB is diameter of circle and angle ACB is leaning on diameter AB.

It signifies that the angle ACB is 90 degree angle and the triangle ABC is right-angled triangle.

Since the angle CAB is 30 degree,  therefore the other acute angle is 90-30 = 60 degree.

Thus the triangle ABC is (30 - 60 - 90) degree triangle.

Since side BC opposite to 30 degree is given as 7 ft, therefore hypotenuse side AB is twice than BC, i.e. 14 ft.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.