Given line m is parallel to line n. What theorem or postulate justifies the statement? ∠1 ≅ ∠4 Corresponding angles postulate Al
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Answer:
There are 16 yellow houses in the neighborhood.
Step-by-step explanation:
We have that:
2/5 = 40% of the houses are painted yellow
1 - 2/5 = 3/5 = 60% of the houses are not painted yellow
If there are 24 houses that are not painted yellow, how many yellow houses are in the neighborhood?
The first step is finding the total number of houses in the neighborhood.
We have that 24 are not painted yellow, and this is 60%(0.6 decimal). How much is 100%?
We solve a rule of three
24 houses - 0.6
x houses - 1
There are 40 houses. Of those, 40% are painted yellow.
0.4*40 = 16.
There are 16 yellow houses in the neighborhood.
The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as
.
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
Now we can use the law of sines to find the distance between Paul and Jose:
Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
We can conclude that Jose is 33.9m from the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
Now we can use the law of sines to find the distance
Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
We can conclude that Jose is 33.9m from the base of the tree.