A mine shaft is dug into the side of a mountain at an angle of depression of 30°. On the other side of the mountain, 6.4 km away, a second shaft is dug at an angle of depression of 45°. How long will each shaft be when they meet? Include a labeled triangle in your solution.

Q: In the evening, a tree that stands 12 ft tall casts a long shadow. If the angle of depression from…

A: Since, it is given that in the evening a 12 ft tall tree cast a long shadow,Also, it is given that…

Q: The top of the slide is 12 feet from the ground and has an angle of depression of $53\degree$53°​ .…

A:

Q: As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65°…

A: A ladder 5 feet long leans against a wall and makes an angle 65° with the ground.we have to find…

Q: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

A: We use Trigonometry ratios to solve this Question

Q: The hypotenuse of triangle ABC has a length of 5. For angle A, the opposite side BC has a length of…

A:

Q: From the top of a 220-ft lighthouse, the angle of depression to a ship in the ocean is 24°. How far…

A:

Q: From a point on the ground 13 feet from the base of a flagpole, the angle of elevation to the top of…

A:

Q: From the earth, the moon subtends an angle of approximately 0.5°. If the distance to the moon is…

A:

Q: Consider a right triangle with a side of length z opposite angle A, a side of length y opposite…

A: According to the given data, the rough sketch of the right-angled triangle is: And, given that,

Q: 3.) A window washer needs to reach a second story window whose sill is 18 feet high. He places a…

A:

Q: A man standing near a building notices that the angle of elevation to the top of the building is…

A: answer is in next step

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: From the earth, the moon subtends an angle of approximately 0.5°. If the distance to the moon is…

A:

Q: The length of a shadow of a building is 9 m. The distance from the top of the building to the tip of…

A: Given that the length of a shadow of a building is 9 m. The distance from the top of the building to…

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

A:

Q: With the sun at a certain altitude, it is noticed that a tower casts a shadow 110 feet long at the…

A:

Q: In the design of a new building, a doorway is 2.65 ft above the ground. A ramp for the disabled, at…

A:

Q: Consider a right triangle with a side of length æ opposite angle A, a side of length y opposite…

A:

Q: A boat sailing due west toward a point y = 160 feet directly north of you makes an angle of 48°, as…

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

Q: A 6-meter long ladder is leaning against a wall. If the top of the ladder makes an angle of 45…

A:

Q: From the observation deck of a skyscraper, Deion measures a 48° angle of depression to a ship in the…

A: Topic = Trigonometric ratios

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: The angle of elevation to a nearby tree from a point on the ground is measured to be 73°. How tall…

A:

Q: A surveyor in an airplane travelling east sees a lake in front of her. The angle of depression to…

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: The dorsal fin of a shark forms an obtuse triangle with the measurements shown in the diagram. Round…

A: We know that the sum of angles in a triangle is 180 degree…

Q: A kite is 50 feet high when 170 feet of string is out. What angle does the kite make with the ground…

A:

Q: A 35-m tall building casts a shadow. The distance from the top of the building to the tip of the…

A: Given that     A 35 m tall building casts a shadow. The distance from the top of the building to the…

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A:

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

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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: 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: The radius of a circle is 13.2 inches. Find the length of an arc of the circle intercepted by a…

A:

Q: From the top of a lighthouse 96 feet high, the angle of depression to a small boat is 37.1658°. How…

A: Follow the procedure given below.

Q: A 34-m tall building casts a shadow. The distance from the top of the building to the tip of the…

A: In this question to find out the length of shadow we use pythagorus theorem.

Q: From the top of a 200 meters high building, the angle of depression to the bottom of a second…

A: Given- From the top of 200 m high building, the angle of depression to the bottom of a second high…

Q: A 16 foot ladder leaning against a wall of a house makes a 50° angle with the ground. How far up the…

A: given: A 16 foot ladder leaning against a wall of a house makes a 50° angle with the ground. we have…

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 bottom of a doorway to a building is 3.45 feet above the ground, and a ramp to the door for the…

A:

Q: A 20-foot ladder is leaning up against a wall. The angle formed with the base of the ladder and the…

A:

Q: Atunnel under a river is 197.3 ft below the surface at its lowest point, as shown in the drawing. If…

A:

Q: From the top of a 220-ft lighthouse, the angle of depression to a ship in the ocean is 28°. How far…

A:

Q: Find the measure of the central angle of an arc if its length is 14n and the radius is 18 m.

A:

Q: The hypotenuse of a right triangle measures 2v15 centimeters and its shorter leg measures 26…

A:

Q: Consider a right triangle with a side of length a opposite angle A, a side of length y opposite…

A: given: A right triangle with a side of length x opposite angle A, a side of length y opposite angle…

Q: From the observation deck of a skyscraper, Bashir measures a 45° angle of depression to a ship in…

A: From the observation deck of a skyscraper, Bashir measures a 45° angle of depression to a ship in…

Q: in a right triangle angle theta has a cosine value of 0.755. The sidebadjacent to angle theta has a…

A: given,       and cosθ=0.755

Q: A 33-m tall building casts a shadow. The distance from the top of the building to the tip of the…

A: Given , Height to building = 33 mand Distance from the top to the building tothe tip to the shadow =…

Q: A 20-foot ladder is leaning up against a wall. The angle formed with the base of the ladder and the…

A:

Q: From the observation deck of a skyscraper, Jamal measures a 51° angle of depression to a ship in the…

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.