In ΔQRS, q = 9.4 cm, r = 8 cm and ∠S=151°. Find ∠Q, to the nearest 10th of a degree.
1 answer:
9514 1404 393
Answer:
15.7°
Step-by-step explanation:
The law of cosines can be used to find side s:
s² = r² +q² -2rq·cos(S)
s² = 8² +9.4² -2(8)(9.4)·cos(151°) ≈ 283.903
s ≈ 16.849
Then the law of sines can be used to find angle Q.
sin(Q)/q = sin(S)/s
sin(Q) = (q/s)sin(S)
Q = arcsin(q/s·sin(S)) = arcsin(9.4/16.849·sin(151°)) ≈ 15.692°
Angle Q is about 15.7°.
You might be interested in
Answer:
27 and 32.
Step-by-step explanation:
Let the two numbers be A and B.
The larger number (let's use B) is 5 more than the smaller one (A). In other words:
Their sum is 59. So:
This is a system of equations. Solve by substituting the first equation into the second. Thus:
Combine like terms:
Subtract 5 from both sides:
Divide both sides by 2:
So, the smaller number is 27.
This means that the bigger number is 27+5=32.
So, the two numbers are 27 and 32.
And we're done!