For the following exercises, use a calculator to find the length of each side to .....A 200-foot tall monument is located in the distance. From a window in a building, a person determines...

For the following exercises, use a calculator to find the length of each side to four decimal places.

A 200-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 15°, and that the angle of depression to the bottom of the tower is 2°. How far is the person from the monument?

Solutions

Expert Solution

The problem can be described by the figure below.

Point A is the point of observation. C denotes the bottom of the monument and B the top. The distance AD is to be calculated whereas the length BC is the height of the monument that is 200 feet.

The height of the monument is the sum of lengths BD and CD which are related to the distance AD by the definition of the tangent of an angle in a right angled triangle.

tan A = length of side opposite to A/length of side adjacent to A

Thus,

tan 15° = BD/AD, tan2° = CD/AD

The length BC is thus,

BC = BD + CD

200 = ADtan15° + ADtan2°

AD = 200/(tan15° + tan2°)

= 660.3494

The distance between the person and the monument is thus approximately 660.35 feet.

Junaid answered 1 year ago

Next > < Previous

Related Solutions

A 400-foot tall monument is located in the distance. From a window in a building, a person determines ...For the following exercises, use a calculator to find the length of each side to four decimal places.

For the following exercises, use a calculator to find the length of each side to four decimal places.A 400-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is 18°, and that the angle of depression to the bottom of the monument is 3°. How far is the person from the monument?

There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the....For the following exercises, use a calculator to find the length of each side to four decimal places.

For the following exercises, use a calculator to find the length of each side to four decimal places.There is an antenna on the top of a building. From a location 300 feet from the base of the building, the angle of elevation to the top of the building is measured to be 40°. From the same location, the angle of elevation to the top of the antenna is measured to be 43°. Find the height of the antenna.

Find the distance from (2, −7, 7) to each of the following. (a) the xy-plane (b)...

Find the distance from (2, −7, 7) to each of the following. (a) the xy-plane (b) the yz-plane (c) the xz-plane (d) the x-axis (e) the y-axis (f) the z-axis

For the following exercises, find the area of each triangle. Round each answer to the nearest tenth. communications tower is located at the top of a steep hill, as shown in Figure 30. The angle ..

For the following exercises, find the area of each triangle. Round each answer to the nearest tenth.A communications tower is located at the top of a steep hill, as shown in Figure 30. The angle of inclination of the hill is 67°. A guy wire is to be attached to the top of the tower and to the ground, 165 meters downhill from the base of the tower. The angle formed by the guy wire and the hill is 16°....

Subjects