The most powerful lighthouse on Lake Michigan is 50 m tall. Suppose you are in a boat just off the coast. Determine your distance from the base of the lighthouse if the angle from the boat to the top of the lighthouse is 14°.

Q: A passenger lift runs 680 ft up the side of a mountain from the base to an exit station. If the…

A:

Q: A dog looks up at a cat who has climbed a 29 foot tree. If the dog is 59 feet from the base of the…

A: The relation between the angles of a triangle and the sides of the triangle is given by the…

Q: An observer is 120 ft from the base of a television tower, which is 150 ft tall. Find the angle of…

A: Given query is to find the angle of elevation.

Q: A person standing 234 feet from the base of a church observed the angle of elevatlon to the church's…

A:

Q: On a test flight, during the landing of the space shuttle, the ship was 366 ft above the end of the…

A:

Q: A person standing 251 feet from the base of a church observed the angle of elevation to the church's…

A:

Q: Find the angle that an 18-foot ladder leaning against a wall makes with the ground If the bottom of…

A:

Q: Jeriel leans a 26-foot ladder against a wall so that it forms an angle of 61° ground. What's the…

A: Given query is to find the distance between base of the ladder and the wall.

Q: When a six-foot pole casts a four-foot shadow, what is the angle of elevation of the Sun? Round to…

A: A six-foot pole casts a four-foot shadow. Now the diagrammatic representation is,

Q: What is the angle of elevation from the ground to the top of a 45-ft tree from 65 feet away? Round…

A: Given,          The ground to the top of a 45-ft tree from 65 feet away.

Q: A 39-foot long escalator is intended to carry people a height of 11 feet. During construction, at…

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Q: Suppose a 15-foot ladder leans against the side of a house so that the angle of elevation of the…

A: The objective is to find the distance of the base of the ladder from the side of the house.

Q: A woman is standing on an 85-meter tall cliff.  She spots a boat in the water below at an angle of…

A:

Q: A building 230 feet tall casts a 40-foot-long shadow. If a person stands at the end of the shadow…

A:

Q: A man who is 70 inches tall casts a shadow of 105 inches. Assuming that the man is standing…

A: Proceed as shown below

Q: Find the angle that an 18-foot ladder leaning against a wall makes with the ground if the bottom of…

A: Here use we have to use trigonometric ratio to find the angle required.

Q: A tree casts a shadow of 14.7 meters when the angle of elevation of the sun is 13.1 degrees. How…

A: A tree shadow of 14.7 meters  angleof elevation of the sun is 13.1 degrees. To find :- Height of a…

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: A 107 feet tall building casts a shadow of 90 feet. To the nearest whole degree, what is the angle…

A: Given: -

Q: An eagle spotted a mouse 20 feet below at an angle of 42 degrees with the horizon. If the eagle…

A: From the given problem, The mouse is 20 feet below the horizon, sp EM = 20 feet The angle of…

Q: The top of an 8-foot ladder leans against a wall at a height of 7 feet. What angle (degrees) does…

A: Length of the ladder is 8 foot and length of the wall is 7 feet. We have to find the angle between…

Q: A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the…

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Q: 3. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: If your standing on the trail 220 feet from the bottom of a tree, you have to look up at a 60 degree…

A: Topic-hight & distance trigonometry

Q: A building 150 feet tall casts a 30 foot long shadow. If a person looks down from the top of the…

A: Given,

Q: A person standing 188 ft from the base of a church observed the angle of elevation to the church's…

A: Given:  The person standing 133 ft from the base of church observed the angle of elevation to the…

Q: 1) Charlie is standing 250 feet from the base of a tall building. If he determines that the angle of…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: A small plane takes off from an airport and begins to climb at a 10.08 angle of elevation at 5,000…

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Q: From the top of a tower 23 m high, a princess looks down at an angle of depression of 70 degrees.…

A: here we need to find the distance bc and ac. the solutio is following.

Q: Jazmin is flying a kite, but it got caught at the top of a 24 ft tree. If she let out 100 ft of…

A:

Q: . The Sears Tower in Chicago is 1454 feet tall and is situated about 1 mile inland from the shore of…

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Q: The leaning tower of Pisa in Italy is 55.9 m tall and is leaned at an angle of 86˚ with the ground.…

A:

Q: A surveyor set up his instrument at A and measured the angle of elevation of the top of a tower and…

A:

Q: A man wants to determine the height of a light house. He measured the angle from the ground and…

A: Given   tan A=3/4 Distance from base of light house to A is 40m .  We have to find height of light…

Q: A 6-meter long ladder is leaning against a wall. If the top of the ladder makes an angle of 450 with…

A: A 6-meter long ladder is leaning against a wall. If the top of the ladder makes an angle of 450 with…

Q: If the shadow cast by a 600 feet tall tree is 1648.48 feet, find the angle (to the nearest tenth of…

A: Let AB represents the tree and BC represents the shadow, Then angle C is the angle of elevation of…

Q: A building 34.65 feet tall has a shadow that is 38.65 feet long. Find the angle of elevation of the…

A:

Q: O A woman 1.65 m tall stood 50 m away from the foot of a tower and observed that the angle of…

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

Q: An observer saw a canoe 8 meters below the cliff that makes a viewing angle with respect to the…

A: Given conditions can be drawn as follows, Here, Angle of depressions 30o and angle ABC are…

Q: A person in a small boat, offshore from the vertical cliff known to be 100 feet in height, takes a…

A: Given  It has to find distance from a person to base of plateau. Here p=100 feet's

Q: A surveyor measured the angle of elevation of a flat spire as 15⁰ from a point on horizontal ground.…

A: Given data is : Angle of elevation of a flat spire as 15∘ from a point on horizontal ground. He…

Q: What is the angle of elevation to the nearest tenth of a degree to the top of a 35-ft building from…

A: Let the angle of elevation to the building be θ. The height of the building = 35 ft.

Q: A building 290 feet tall casts a 100 foot long shadow. If a person stands at the end of the shadow…

A: Given,Height of building = 290 feetShadow length = 100 feetThe person’s height = 5 feet

Q: Janelys leans a 16-foot ladder against a wall so that it forms an angle of 61° with the ground. How…

A: Here AC = length of ladder = 16 foot AB = wall BC = ground m∠ACB = 61° We have to find the length of…

Q: How tall is a building that casts a 75​-ft shadow when the angle of elevation of the sun is 35°​?

A: height of building =?

Q: If you stand 100 feet from the gym, how tall would it be if the angle of elevation feet to the top…

A: Lets assume that the gym is x feet tall . Drawing the Diagram as per  the Question , Let OA…

Q: Find x, the angle of depression from the top of a lighthouse that is 151 ft above water level to the…

A:

Q: Suppose your angle of elevation to the top of a water tower is 78°. If the water tower is 145 ft…

A: Here we will use the concept of trigonometry and find the solution. We have to find the distance…

Q: A person 100 meters from the base of a tree, observes that the angle between the ground and the top…

A:

Q: The cables attached to a TV relay tower are 100 m long. They meet level ground at an angle of 60.0°,…

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.