Peter has three pieces of wood. Board A is 7 inches long, board B is 14 inches long, and board C is 5 inches long. If the full length of each board is used, can the three pieces of wood be placed together to form a triangle?
A. yes, 14 - 7 > 5
B. yes, 5 + 7 < 14
C. no, 7 + 5 < 14
D. no, 14 - 5 < 7

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

a:

step-by-step explanation:

a