now, if we a "prime factoring" of each number, we get
204 =
2*2*3*17
120 = 2*
2*2*3*5
168 = 2*
2*2*3*7
now, notice the GCD for all three is that common bolded values, namely 2*2*3, or 12, so each room will house 12 participants,
now, how many rooms for all German? 204 ÷ 12, or 17 rooms.
how many rooms for all English ones? 120 ÷ 12, or 10 rooms.
how many rooms for the French ones? 168 ÷ 12, or 14 rooms.
so the total amount of rooms for all of them is
17 + 10 + 14.
Answer: The measure of ∠SQR= 80.9°
Step-by-step explanation:
Given: In triangle QRS,
∠ RSQ = 29.1° and ∠QRS=70°
To find: ∠SQR
Angles sum property of triangle = Sum of all the angles in a triangle is 180°.
For Δ QRS,
∠SQR + ∠ RSQ +∠QRS = 180°
⇒ ∠SQR + 29.1° + 70° = 180°
⇒ ∠SQR + 99.1° = 180°
⇒ ∠SQR= 180°-99.1
⇒ ∠SQR= 80.9°
Hence, the measure of ∠SQR= 80.9°
9514 1404 393
Answer:
2
Step-by-step explanation:
The given angle is opposite the shorter of the given sides, so there are two possible triangles.
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<em>Additional comment</em>
The law of sines tells you that sin(A) = a/c·sin(C). There will be 0 triangles if that is greater than 1. There will be 1 triangle if that is exactly 1 (unlikely with rational values of sides and angles). There will be 2 triangles if sin(A) < 1, as it is here.
It totals out to 2496 in^2
Hope this helped