In triangle PQR, m angle R = 32, p = 21, and q = 21. what is side lenth r? explain each step

11.577 = r

Step-by-step explanation:

Comment

When you draw a sketch of this, <R is between p and q - - both of which are lines. The Cos law is the one you use.

Equation

r^2 = p^2 + q^2 - 2pq * Cos(R)

Givens

p = 21

q = 21

R = 32

r = ?

Solution

r^2 = 21^2 + 21^1 - 2*21*21 * Cos(32)     Substitute givens into the equation

r^2 = 441 +441 - 882 * 0.8480               Add the first two terms.

r^2 = 882 - 747.98                                 Multiply Cos(32)  by 2 * 21 * 21

r^2 = 134.02                                            Subtract 747.98 from 882

sqrt(r^2) = sqrt(134.02)                           Take the square root of both sides.

r = 11.577

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

1 1/7 hope i

step-by-step explanation:

8/7 = (1 * 7 + 1) / 7 = 1 + 1/7 = 1 1/7