Peter needs a ladder to get to his roof for a repair. In order for the ladder to be the most stable, it must be positioned at a 30 degree angle. If his roof is 20 feet off the ground, how long must his ladder be? (Round to the nearest tenth, if necessary.)

Q: Two surveyors, Warren and MJ, need to determine the height of a steep cliff. They stand 50 m apart…

A: Two surveyors, Warren and MJ, need to determine the height of a steep cliff. They stand 50 m apart…

Q: Donte is standing on top of a 50 foot building and sees his friend, Molly. If Molly is 30 feet away…

A:

Q: Rapunzel is at the top of her tower, looking down at Flynn rider who is running towards the base of…

A: QUESTION- Rapunzel is at the top of her tower, looking down at Flynn rider who is running towards…

Q: How high does a 17-foot-tall temporary support post reach when it is positioned at a 30° angle to…

A: Let height be h and we know that in a right angle triangle  sinθ=side opposite to…

Q: Haley planted a new tree in her yard.  To help the tree to grow upright, she attached support wires…

A:

Q: From the third floor window of a building the angle of depression of an object on the ground is 35°…

A: Given that the angle of depression of an object on the ground from third floor window of a building…

Q: From the top of a 550-foot cliff, a hiker looks down at a river below. Her angles of depression to…

A:

Q: Ron and Harry, who are 40 ft apart, are watching a Quidditch match. If the angle of elevation from…

A: topic - application of trigonometry

Q: The height of a radio tower is 800ft, adn the ground on one side of the tower sloped upward at an…

A:

Q: Use the fact that the longest side of a triangle is across from the largest angle to explain why the…

A: Here we have to prove that the hypotenuse is always the longest side in the right triangle.

Q: Find the measure of an angle that is twice as large as its supplement.

A: Given: Let the required angle be 2x and the supplement angle be x

Q: The angle from the tee box to the green is 30° on a par 3, 185 yard hole as shown. How much higher…

A:

Q: A homeowner is to construct a ramp to his front door to make it wheel-chair accessible. How long is…

A:

Q: The base of a ladder is 6 ft from the building, and the angle formed by the ladder and the ground is…

A:

Q: Two observers A and B who are 462m apart find at the same instant that the angles of elevation of a…

A: Given that , AB=462 m find altitude h=?

Q: From a second storey of a building window directly across the street, the angle of elevation of the…

A:

Q: The height of a radio tower is 650 feet, and the ground on one side of the tower slopes upward at an…

A: Let the angle between the tower and the slope be theta.The angle between the tower and the base is…

Q: A 14-foot ladder is being used to get to the top of a 12-foot-tall wall. At what angle of elevation…

A:

Q: The height of a radio tower is 750 feet, and the ground on one side of the tower slopes upward at an…

A: The objective is to find the lengths of first and second guy wire.

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L=1350 feet apart. As the…

A:

Q: Gabe can see the top of the fountain by looking up at an angle of 39o . If Gabe is 1.3m tall and the…

A: Given that Gabe can see the top of the fountain at an angle of 39 degree. If Gabe is 1.3 m tall and…

Q: A bike is 80 long and has an end height of a 3 feet, as shown below. what is the measure of angle…

A:

Q: What is the angle of Angle A in a right triangle whose hypotenuse is 23cm and opposite side is 12cm?

A: Please see the diagram on the white board. It aptly explains the question. ABC is the triangle right…

Q: A 100-foot vertical tower is to be erected on the side of a hill that makes a 6° angle with the…

A: ANSWER IS AS FOLLOWS:

Q: Bob, who is 2.2 m tall, is standing a distance of 15 m from a flagpole as shown below. From his…

A: Consider a point A on the flag pole such that point B and A are at the same level from the ground.…

Q: Determine the length of a ladder needed to reach the roof of the building shown below. The building…

A:

Q: Alayna is trying to determine the angle at which to aim her sprinkler nozzle to water the top of a…

A: Distance between tree and sprinkler = 4ft  Height of tree= 5ft

Q: A boy flying his kite releases the entire length of his string which measures 26 m, so that the kite…

A: Find the solution below

Q: You are putting together the frame of a fence gate as shown below: If the width of the frame is 3…

A: We know in a right angle triangle the formula of Pythagoras theorem is,…

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

A:

Q: A person standing d = 153 centimeters from a mirror notices that the angle of depression from his…

A: Consider a right-angled triangle as shown in the figure. The trigonometric ratios for the given…

Q: Jan measures the angle of elevation of the peak of the mountain at 35 degrees. Susan, who is 1200…

A:

Q: Two gears are adjusted so that the smaller gear, with a radius of 12.4cm, drives the larger one. If…

A:

Q: The height of a radio tower is 680 feet, and the ground on one side of the tower slopes upward at an…

A: We have to find the length of wire.

Q: An escalator in a department store rises 80 feet at a 32° angle, as shown below. 80 feet What is the…

A: It is a right angle triangle so  SinA = opposite side/ adjacent side Given A =32o And opposite side…

Q: A player takes a shot 22 ft. away from the base of the goal but the puck hits the top of the goal…

A: A player takes a shot 22 ft. away from the base of the goal but the puck hits the top of the goal…

Q: A lot is in the shape of a triangle whose two sides measure 150 m and 100 m, with the angle between…

A:

Q: An American-Italian high school hockey player from the North Shore is standing 10 feet from a…

A:

Q: Alexander is looking up at a 43-foot tall building at an angle of elevation of 28°. If his eyes are…

A:

Q: Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high. If the sides of the tent…

A:

Q: - Jaden is flying a kite and lets off 275 feet of string. If the kite is 150 feet above ground and…

A:

Q: Maria is to weld a support for a 27 m conveyor so that it will operate at a 20 degree angle. What is…

A: Multiply both for length of support

Q: For safety, the angle of a wheelchair ramo makes with the horizontal should be no more than 3.5…

A: Consider the figure given below :

Q: The builder of a parking garage wants to build a ramp at an angle of 12 that covers a horizontal…

A:

Q: Michelle is stadning on the rooftop of the seda hotael, looking at abreeza mall in the distance. The…

A: According to the given problem, the representative diagram is shown below; Let  the distance from…

Q: Two buildings with flat roofs are 15 m apart. From the edge of the roof of the lower building, the…

A:

Q: I have a ridiculous number of trees and shrubs that need pruning in my yard. I have a 15 foot ladder…

A: Given: The ladder is 15 foot and angle between ladder and the ground is 70°. To find the height up…

Q: A hot-air balloon is floating above a straight road. To calculate their height above the ground, the…

A: Given that a hot-air balloon is floating above a striaght road angles of depression are 21° and 23°…

Q: A kite is flying at a 28° angle on a 300 ft string. Assuming the string is straight,how high is the…

A:

Q: Dean is on a 70 m high bridge and sees two boats anchored at points C and D below. Dean estimates…

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.