To find the height of a mountain, surveyors often find the angle of elevation to the top from two points at the same altitude a
fixed distance apart. Suppose that the angles of the elevation from two points 500 meters apart are 35.333333333 degrees and 25.766666666666 degrees. How high is the mountain above the altitude of the two points
1 answer:
Answer:
756.36 meters
Step-by-step explanation:
Draw a diagram. Let's call the horizontal distance from the top of the mountain to the closest point x.
Using tangent = opposite / adjacent, we can write two equations:
tan 35.3° = h / x
tan 25.76° = h / (x + 500)
Solve for x in the first equation and substitute into the second.
x = h / tan 35.3°
tan 25.76° = h / ((h / tan 35.3°) + 500)
Solve for h.
tan 25.76° (h / tan 35.3°) + 500 tan 25.76° = h
500 tan 25.76° = h (1 − (tan 25.76° / tan 35.3°))
500 tan 25.76° tan 35.3° = h (tan 35.3° − tan 25.76°)
h = 500 tan 25.76° tan 35.3° / (tan 35.3° − tan 25.76°)
h ≈ 756.36 meters
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Answer:
B :- 15
Step-by-step explanation:
Given:
A package of red rose contains = 3 pieces
A package of white rose contains = 5 pieces
If an equal number of red and white roses are wanted to make bouquets, what is the minimum number of each that can be purchased ?
Solution:
As here given that there are two types of package of roses, red roses come 3 pieces to each packet and white roses come 5 pieces to each packet and we have to find equal minimum number of red roses as well as white roses to be purchased, we will simply find the Lowest common multiple of 3 and 5.
Multiples of 3 :- 3, 6, 9,12, 15, 18, 21, 24
Multiples of 5 :- 5, 10, 15, 20, 25
<em>Lowest common multiple is 15, that means </em><em>15 is the minimum number of pieces of each that can be purchased to make bouquets.</em>
And number of packets of red rose have to purchase = 3 <em><u>5</u></em> = 15, 5 packages.
And number of packets of white rose have to purchase = 5 <em><u>3</u></em> = 15 , 3 packages.