Two runners in a marathon determine that the, №14813902, 28.05.2020 04:18

Mathematics

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degrees and 42 degrees. if the helicopter is 1950 feet directly above the finish line how far apart are the runners?

Step-by-step answer

P Answered by PhD

See the attached figure to understand the problem

we know that
tan 42°=1950/BO---------> BO=1950/tan 42°-------> BO=2165.69 ft

tan 39.5°=1950/AO---------> AO=1950/tan 39.5°-------> AO=2365.54 ft

AB=AO-BO--------> AB=2365.54 ft-2165.69 ft-------> AB=199.85 ft

the answer is
The runners are 199.85 feet apart

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degre

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degre

Mathematics

Two runners in a marathon determine that the angles of elevation of a news helicopter covering the race are 38 degrees and 45 degrees. If the helicopter is 1700 feet above the finish line, how far apart are the runners? (Round your answer to the nearest foot) *

Step-by-step answer

P Answered by PhD

476 feet

Step-by-step explanation:

The given problem when graphically depicted forms a right triangle which has been attached below.

We want to determine the distance between Runner A and Runner B in the diagram.

Using Trigonometric Ratios

In Right Triangle AHC

$\tan 38^\circ =\dfrac{1700}{AC} \\$Cross multiply$\\AC *\tan 38^\circ =1700\\AC =\dfrac{1700}{\tan 38^\circ}\\\\=2175.9$ feet$

In Right Triangle BHC

$\tan 45^\circ =\dfrac{1700}{BC} \\$Cross multiply$\\BC *\tan 45^\circ =1700\\BC =\dfrac{1700}{\tan 45^\circ}\\\\=1700$ feet$

The distance between the two runners,

AB=AC-BC

=2175.9-1700

=475.9

=476 feet ( to the nearest foot)

Mathematics

Two runners in a marathon determine that the angles of elevation of a news helicopter covering the race are 38 degrees and 45 degrees. If the helicopter is 1700 feet above the finish line, how far apart are the runners? (Round your answer to the nearest foot) *

Step-by-step answer

P Answered by PhD

476 feet

Step-by-step explanation:

The given problem when graphically depicted forms a right triangle which has been attached below.

We want to determine the distance between Runner A and Runner B in the diagram.

Using Trigonometric Ratios

In Right Triangle AHC

$\tan 38^\circ =\dfrac{1700}{AC} \\$Cross multiply$\\AC *\tan 38^\circ =1700\\AC =\dfrac{1700}{\tan 38^\circ}\\\\=2175.9$ feet$

In Right Triangle BHC

$\tan 45^\circ =\dfrac{1700}{BC} \\$Cross multiply$\\BC *\tan 45^\circ =1700\\BC =\dfrac{1700}{\tan 45^\circ}\\\\=1700$ feet$

The distance between the two runners,

AB=AC-BC

=2175.9-1700

=475.9

=476 feet ( to the nearest foot)

Mathematics

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degrees and 42 degrees. if the helicopter is 1950 feet directly above the finish line how far apart are the runners?

Step-by-step answer

P Answered by PhD

See the attached figure to understand the problem

we know that
tan 42°=1950/BO---------> BO=1950/tan 42°-------> BO=2165.69 ft

tan 39.5°=1950/AO---------> AO=1950/tan 39.5°-------> AO=2365.54 ft

AB=AO-BO--------> AB=2365.54 ft-2165.69 ft-------> AB=199.85 ft

the answer is
The runners are 199.85 feet apart

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degre

Mathematics

Two runners in a marathon determine that the angles of elevation of a news helicopter are 39.5 degrees and 42 degrees. if the helicopter is 1950 feet directly above the finish line how far apart are the runners?

Step-by-step answer

P Answered by PhD

For a given angle of elevation θ, the distance from the runner to the finish lline is
.. d = 1950×cot(θ)

The difference in distance to the finish line is the distance between runners, so that distance is
.. d₁ -d₂ = 1950×(cot(θ₁) -cot(θ₂)
.. = 1950×(cot(39.5°) -cot(42°))
.. ≈ 200 . . . . feet

The runners are about 200 feet apart.

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180