Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar
2 answers:
Answer: 2.8 inches
Step-by-step explanation:
Given : The beams intersect each other to form two similar triangles ΔQRP and ΔARC .
PR = 3.4 inches
CR = 5.1 inches.
AC = 4.2 inches
To find : PQ
We know that the corresponding sides of two similar triangles are proportional.
i.e. for similar triangles ΔQRP and ΔARC , we have
Hence, the distance between the endpoints of the beams P and Q = 2.8 inches
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Answer and Step-by-step explanation:
You are correct in that we need to use the Law of Sines: .
Here, when we use the Law of Sines, we have: .
Cross multiply:
(sinB) * 28 = (sin63) * 29
28sinB ≈ 25.839
sinB ≈ 0.9228
Now, in order to solve for B, we need to use inverse sin ():
The sines on the left cancel out, and we're left with:
B ≈ 67.3 degrees
Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:
180 - 67.3 = 112.7 degrees.
Hope this helps!
<h3>Answer: Parallelogram</h3>
You could use the parallelogram rule to add the vectors, or you could use the tip-to-tail method (your textbook might call it the "head to tail method" but it's the same idea).
An example of the parallelogram method is shown below with adding the vector u = (-4,4) in red to the vector v = (8,2) in blue to get the vector w = (4,6) in green. The green resultant vector is one of the diagonals of the parallelogram
Side note: The other diagonal is either u-v or v-u depending on your reference point.