Each leg of a 45°-45°-90° triangle measures 12 cm. what is the length of the hypotenuse?

 The length of the hypotenuse is 12√2 units.

Step-by-step explanation:  As shown in the attached figure below, the triangle ABC is a right-angled one, where

m∠B = 90°, m∠A = m∠C = 45°   and   AB = BC = 12 cm.

We are to find the length of the hypotenuse, AC.

From Pythagoras theorem, we have

Thus, the length of the hypotenuse is 12√2 units.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.