2. Janet baby-sat for 28 hours over two weeks. She earned $5.00 an hour. What was her gross pay?
2 answers:
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Answer:
Step-by-step explanation:
Since AC || DE, and ABC forms a triangle, we can deduce that ABC is a smaller triangle inside triangle DBE.
In the second step, we see that ∠CAB in the smaller triangle is congruent to ∠EDB in the larger one, due to the corresponding angles theorem. We also see that ∠ACB in the smaller triangle is congruent to ∠DEB in the larger one, again by the corresponding angles theorem.
This leads to the third step; since we have two of the angles in one triangle congruent to the corresponding angles in the other triangle, this means the third angle will be congruent (since all triangles equal 180°, and the first two angles are equal, the third must be equal as well). Two triangles in which all three angles of one triangle are congruent to the three angles of the other are similar triangles.
Since the triangles are similar, corresponding sides have the same ratio. This means that the ratio of AB to the larger side DB is the same as the ratio of CB to the larger side EB; this gives us
AB/DB = CB/EB.
Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
