MATHEMATICS HIGH SCHOOL

Looking north, two skyscrapers are sighted from the viewing deck of the Empire State Building at 1250 feet up. One skyscraper is sighted at a 20° angle of depression and a second skyscraper is sighted at a 30° angle of depression. How far apart are the two skyscrapers to the nearest foot?

Answers

Answer 1

Answer:

The angle of depression is the angle between the line of sight and a vertical line.

The distance between the two skyscrapers is 1269ft

I've added as an attachment, a figure that illustrates the scenario

First, we calculate distance AB using the following tangent ratio

$\mathbf{\tan(\theta) = (Opposite)/(Adjacent)}$

So, we have:

$\mathbf{\tan(60) = (AB)/(1250)}$

Make AB the subject

$\mathbf{AB = 1250 * \tan(60)}$

Next, we calculate distance AC using the following tangent ratio

$\mathbf{\tan(\theta) = (Opposite)/(Adjacent)}$

So, we have:

$\mathbf{\tan(60+10) = (AB + BC)/(1250)}$

$\mathbf{\tan(70) = (AB + BC)/(1250)}$

Make AB + BC, the subject

$\mathbf{AB + BC = 1250 * \tan(70)}$

Make BC the subject

$\mathbf{BC = 1250 * \tan(70) - AB}$

Substitute $\mathbf{AB = 1250 * \tan(60)}$

$\mathbf{BC = 1250 * \tan(70) - 1250 * \tan(60)}$

$\mathbf{BC = 1269}$

Hence, the distance between the two skyscrapers is 1269ft

Read more about angles of depression at:

brainly.com/question/13697260

Answer 2

Answer:

Answer:

Step-by-step explanation:

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A school has ordered 16 buses that each have 40 seats for a school trip. There are 32teachers and 576 students. Each bus must have 2 teachers and the rest students. If the
students are distributed evenly amongst the buses, how many students would be on each
bus? How many empty seats will there be in total?

Answers

36 students will be in each buses for the trip.

The total number of empty seat in the buses is 32

How to find the total number of seats?

The school ordered 16 buses that each have 40 seats for a school trip.

There are 32 teachers and 576 students.

Each bus must have 2 teachers and the rest students.

The students were distributed evenly amongst the buses.

Therefore,

number of student in each buses = total number of student / number of buses

number of student in each buses = 576 / 16

number of student in each buses = 36

Therefore, 36 students will be in each buses for the trip.

Each buses has 40 seats.

Recall, 2 teachers are even distributed in each buses.

Therefore

number of empty seat in total = 16 × (40 - 36 - 2)

number of empty seat in total = 16 × 2

number of empty seat in total = 32

Therefore, the total number of empty seats in the buses is 32.

learn more on algebra(total number) here: brainly.com/question/13875201

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