Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Jillian is a firefighter. She stands at an observation window $85$ ft above the ground. From a distance, she spots a fire! She takes a reading -- and she sees that the angle of depression is $28^\circ$ . To the nearest tenth of a foot, how far away from the base of the tower is the fire?

View step-by-step help

View step-by-step help

Pythagorean theorem

Full solution

Q. Jillian is a firefighter. She stands at an observation window

85

ft above the ground. From a distance, she spots a fire! She takes a reading -- and she sees that the angle of depression is

28^\circ

. To the nearest tenth of a foot, how far away from the base of the tower is the fire?

Identify Relationship: Identify the relationship between the angle of depression and the angle of elevation. $\newline$ The angle of elevation from the base to Jillian's eyes is also $28^\circ$ because angles of elevation and depression are congruent.
Use Tangent Function: Use the tangent function, which relates the opposite side (height of the tower) to the adjacent side (distance from the base of the tower to the fire). $\newline$ $\tan(28^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{85}{\text{distance}}$
Solve for Distance: Solve for the distance by multiplying both sides by the distance and then dividing by $\tan(28°)$ . $\newline$ $\text{distance} = \frac{85}{\tan(28°)}$
Calculate Distance: Calculate the distance using a calculator. $\newline$ distance = $85 / \tan(28°) \approx 85 / 0.5317 \approx 159.9$ feet

More problems from Pythagorean theorem

Question

A multi-layer cake is in the shape of a right cylinder. The height of the cake is

20

(\mathrm{cm})

, and its radius is

10 \mathrm{~cm}

. If each of the cake layers has a volume of approximately

1

250

cubic centimeters, then how many layers does the cake have?

Posted 26 days ago

Question

A right pyramid with a square base has a volume of

252

cubic centimeters. The length of one of the sides of its base is

6

centimeters. Rounded to the nearest centimeter, what is the vertical height of the pyramid?

Posted 1 month ago

Question

\mathrm{Ji}

-Hun and Kana are running a marathon. Due to the volume of people running, the starts occur in waves. Kana starts at

9: 35

\mathrm{a} . \mathrm{m}

. and runs at an average rate of

7

miles per hour (mph). Ji-Hun starts at

10: 00

\mathrm{a} . \mathrm{m}

. and runs at an average rate of

8 \mathrm{mph}

. Assuming constant paces and no stops, to the nearest tenth of a mile, in how many miles will Ji-Hun catch up to Kana?

Posted 1 month ago

Question

Imani's grandmother's house is

5

miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at

10

miles per hour. Which equation best describes the distance,

d

, in miles, Imani is from home after

t

\newline

1

\newline

d=5+10 t

\newline

d=5-10 t

\newline

d=5 t+10

\newline

d=5 t-10

Posted 1 month ago

Question

Mr. Mole left his burrow and started digging his way down.

\newline

A

represents Mr. Mole's altitude relative to the ground (in meters) after

t

\newline

A=-2.3 t-7

\newline

How far below the ground does Mr. Mole's burrow lie?

\newline

meters below the ground

Posted 1 month ago

Question

To get to school, Da'Quon walks

0

6

miles from his house to the bus stop. He then takes the bus for

3

9

miles. After he gets off the bus, he can choose one of several walking routes to school. The total number of miles he travels, via walking and bus, does not exceed

5

4

. What is the greatest possible number of miles he walks after getting off the bus?

\newline

1

\newline

0

0

\newline

0

3

\newline

0

9

\newline

1

5

Posted 2 months ago

Question

The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to

1180

pounds per square inch (psi). Underwater pressure consists of atmospheric pressure, which is

14.7 \mathrm{psi}

0.45 \mathrm{psi}

of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?

Posted 1 month ago

Question

A rectangular prism and cube have equal volumes. The length of the rectangular prism is

12

(\mathrm{cm})

and its width is

8 \mathrm{~cm}

. If each side of the cube is

12 \mathrm{~cm}

, then what is the height of the rectangular prism in centimeters?

Posted 28 days ago

Question

Emeka forms a ball of clay with a radius of

3

(\mathrm{cm})

. He then reforms the clay into a cylinder of radius

2 \mathrm{~cm}

. What is the height of the cylinder in centimeters, rounded to the nearest tenth?

Posted 28 days ago

Question

A cube of gold with an edge length of

3

inches (in) is melted and reformed into a rectangular prism with a width of

2

5

in and a height of

2 \mathrm{in}

. If the volume is unchanged during melting, what is the length of the prism of gold in inches?

Posted 4 months ago