At as distance "X" ft. away from the base of a hill, Mr. Somebody noted that the angle of elevation of the hilltop is 32°20'. Moving closer to the hill, 325 ft in a straight line, the angle of elevation is noted to become 55°40'. How high is the hill? Show figure.

Q: From a window 30 feet above the level ground, a building 100 feet high, and at a distance of 200…

A:

Q: The terminal side of angle α is in quadrant III. What sign, positive or negative, will the sine,…

A:

Q: At a point 200 feet from the base of a building, the angle of elevation to the bottom of a…

A:

Q: A tree casts a 25-foot shadow on a sunny day, as shown in the diagram below. 32 - 25 ft – If the…

A: Solution: The objective is to find the height of the tree

Q: At a point 45 feet from the base of a church, the angles of elevation to the bottom of the steeple…

A:

Q: At a point 50 feet from the base of a church, the angles of elevation to the bottom of the steeple…

A: Given,          At a point 50 feet from the base of a church , the angles of elevation to the…

Q: An airplane traveling 400 mph at a cruising altitude of 6.6 mi begins its descent. If the angle of…

A: Given  Speed of airplane = 400 mph Altitude of airplane (at t=0 min) = 6.6mi Angle of descent = 2°

Q: At 11:30 A.M. the angle of elevation of the sun for Washington, D.C., is 55.7°. If the height of the…

A:

Q: The angle of elevation from a viewer to the top of a flagpole is 50°. If the viewer is 40 feet away…

A: Solution: In ∆ABCtan 50°  =ABBC⇒ tan 50×40 = h                   h = 47.67                   h =…

Q: The top of a 190-foot vertical tower is to be anchored by cables that make an angle of 30° with the…

A:

Q: The angle of elevation to a nearby tree from a point on the ground is measured to be 65∘∘. How tall…

A: given: The angle of elevation to a nearby tree from a point on the ground is measured to be . we…

Q: The angle of elevation to the top of a very tall Building is found to be 11° from the ground at a…

A: Given angle of elevation = 110 horizontal distance = 1 mi = 5280 foot

Q: From a point on the ground 47 feet from the foot of a tree, the angle to the top of the tree is 35…

A: The following diagram depicts the situation, Here AB represents the tree and C is the location of…

Q: The angle of elevation to the top of a very tall building is found to be 15° from the ground at a…

A: The angle of elevation to the top of a very tall building is found to be 15° from the ground at a…

Q: A helicopter takes off, and travels forward at an angle of 65.1°above horizontal. After following…

A:

Q: You are in a tall building and from your window you notice a window washer working on the building…

A:

Q: From the top of a 300 feet tallI lighthouse, the angle of depression to a ship in the ocean is 21°.…

A:

Q: Assuming that a 360-foot tall giant redwood grows vertically, if I walk a certain distance from the…

A:

Q: A loading ramp is 21 meters long with a height of 6 meters. What is the angle of incline that the…

A: Explanation of the answer is as follows

Q: After a hurricane, a homeowner examines trees on his property for damage. He thinks a 21-ft palm…

A: After a hurricane, a homeowner examines trees and thinks a 21-ft palm tree is leaning slightly from…

Q: The angle of elevation to a nearby tree from a point on the ground is measured to be 47°. How tall…

A:

Q: At a point on the ground 54.0m from the foot of a tree, the angle of elevation to the top of the…

A: Given:

Q: The angle of elevation to the top of a Building in New York is found to be 2 degrees from the ground…

A:

Q: ● From a point A the angle of elevation of a post is 460 10' while from a point D, 50 meters from A…

A: Note- As per our guidelines we have to answer only first question if multiple questions are…

Q: An airplane is observed to be approaching a point that is at a distance of 15 km from the point of…

A:

Q: From a point on the ground, the angle of elevation to the top of a vertical wall is 40°. If the wall…

A:

Q: Find x, the angle of depression from the top of a lighthouse that is 188 ft above water level to the…

A:

Q: A​ blimp, suspended in the air at a height of 600 ​feet, lies directly over a line from a sports…

A: The distance between the sports stadium is

Q: Suppose that you are headed toward a plateau 51.8 meters high. If the angle of elevation to the top…

A:

Q: A water tower is located 325ft from a building. From a window on the 10th floor, the angle of…

A: As given in the question distance of water tower is 325 ft from building, the angle of elevation to…

Q: To find the height of a tree, a person walks to a point 30 feet from the base of the tree and…

A: Let height of tree be ABNow in triangle ABCtan 57 = PerpendicularBasetan 57 = ABACAB = 30 tan 57AB =…

Q: From the top of a 167-ft lighthouse, the angle of depression to a ship in the ocean is 20°. How far…

A:

Q: The pilot of a small airplane flying 600 m above the ground notices a village 800 horizontal meters…

A:

Q: An airplane traveling at 600 mph at a cruising altitude of 6.9 mi begins its descent. If the angle…

A:

Q: 1) An airplane is flying at an altitude of 6000 m over the ocean directly toward a coastline. At a…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: From an airplane at an altitude of 1,289 m, the angle of depression to a rock on the ground measures…

A:

Q: From the top of a 163-ft lighthouse, the angle of depression to a ship in the ocean is 21°. How far…

A: Height of the lighthous and angle of depression is given. So first draw the digram then use the…

Q: At 11:30 a.m. the angle of elevation of the sun for one city is 55.9°. If the height of a monument…

A:

Q: The angle of elevation to the top of a very tall Building is found to be 6 degree from the ground at…

A: Given : Angle of elevation = 6°

Q: Find the angle of depression from the top of a lighthouse 400 feet above water level to the water…

A:

Q: The angle of elevation to a nearby tree from a point on the ground is measured to be 47°. How tall…

A: Given that angle of elevation to a nearby tree from a point on the ground is 47° and the tree is 67…

Q: The length of a shadow of a tree is 125 feet when the angle of elevation of the sun is 31°.…

A:

Q: From a point 25 m from the bottom of a maple tree, the angle of elevation to the top of the maple…

A: We use trigonometric ratios to find out the result.

Q: A wind tower at the top of a hill casts a shadow 30 m long along the side - the hill. An observer at…

A:

Q: From a window 33.0 ft above the​ street, the angle of elevation to the top of the building across…

A:

Q: A 16 foot ladder is used to scale a 14.5 foot wall. At what angle of elevation must the ladder be…

A: Please see the answer below.

Q: A pole casts a shadow of 30 ft at one time and a shadow of 15 ft at a later time when the angle of…

A:

Q: The angle of elevation to the top of a flagpole is 40° from a point 30 meters away from the base of…

A: Let the height of the flagpole be h. In a right angled triangle, the tangent of an angle(other than…

Q: At a point 40 feet from the base of a church, the angles of elevation to the bottom of the steeple…

A:

Q: A helicopter is hovering 78 feet above a landing pad. If the man is 81 feet from the landing pad,…

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.