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ra1l [238]
3 years ago
11

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

Mathematics
1 answer:
8090 [49]3 years ago
5 0

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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Solve the math problem
luda_lava [24]

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Step-by-step explanation:

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2 years ago
After driving 152 ​km, 4/5 of a trip is completed. How long is the total​ trip? How many more kilometers must be driven to compl
nikitadnepr [17]

Answer:

1. Total Trip Distance = 190 kilometers

2. To complete the trip, 38 more kilometers left


Step-by-step explanation:

1.

Let total trip be x kilometers.

So we can say

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152=\frac{4}{5}x\\x=\frac{152}{\frac{4}{5}}\\x=190


Total trip is 190 km.


2.

Since already driven 152, to complete 190, you have to drive  190-152=38 kilometers more.

So, 38 more kilometers to complete the trip.

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