The trunk of a tree makes a 60° angle with the ground. A ladder leans against the trunk on the 60°-side. When the top of the ladder is 3 feet from the trunk's base, the bottom end is 12 feet from the base. Let t and b measure the respective distances (in feet) from the base of the trunk to the top and bottom ends of the ladder.

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 boy is 1.5 m tall standing 12 m away from a church building which has a tower on top of its roof.…

A: We are given that a boy is 1.5 m tall standing 12 m away from a church building that has a tower on…

Q: Find the angle 0 between v= 8i- 6j and w=-12i- 5j. If necessary, round to the nearest tenth of a…

A: Given  v=8i-6j w=-12i-5j

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

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

Q: The sides of a parallelogram are 16 m and 10 m, and the longer diagonal makes an angle of 18° with…

A: Let x be the length of the longer diagonal use law of sines to find the value of x from the lower…

Q: Find the angle 0, in radians, in the given right triangle. The length of the side adjacent to 0 is…

A: Given, The triangle is right angled triangle, so formula of Tan theta can be used.

Q: A is located 250 ft from a building. From a window in the building, a person determines that the…

A:

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 300 foot tall monument is located in the distance. From a window in a building a person determines…

A:

Q: Find the angle 0 between v = cos 120°i+ sin 120°j and w= cos 135°i+ sin 135°j. If necessary, round…

A: Given, v=cos120∘i+sin 120∘jw=cos135∘i+sin135∘j We know that, cos…

Q: Find x, the angle of depression from the top of a lighthouse that is 187 ft above water level to the…

A: Angle of depression is 9.6°

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

A:

Q: Use the law of sines to find the measure of the indicated angle

A:

Q: 7) Find the height of a building that projects a shadow of 350 ft on the ground, if the angle of…

A: The height of the building that projects a shadow of 350 ft on the ground  and the angle of…

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

A:

Q: Find the angle between v = -3i + 2j and w = 4i - j. Round to the nearest tenth of a degree.

A: Given v=-3i+2j & w=4i-j We have to find angle between given two vectors. Solution: Let angle…

Q: Use the sine law to determine the length of side a, to the nearest tenth of a cm, given that b =…

A: follow next step

Q: Find the exact values of the sine, cosine, and tangent of the angle 345°

A:

Q: Find x, the angle of depression from the top of a lighthouse that is 156 ft above water level to the…

A: The given figure is: To find x

Q: Consider the following figure: Transit 27.8° 131 ft 5.5 ft From a transit station located 5.5 ft…

A: By trigonometric Identity we solve the following problem

Q: A 18-ft ladder leans against a building so that the angle between the ground and the ladder is 67°.…

A: Ladder = 18 ftangle , θ= 67°

Q: Find the angle between u=2i+j and v=-4i+10j in degrees as a decimal rounded to the nearest hundredth

A:

Q: The angle between 0 and 2T in radians that is coterminal 26 ·T in radians is 9. with the angle |

A:

Q: Find the angle 0 between v= cos 120°i+ sin 120°j and w = cos 135°i+ sin 135°j. If necessary, round…

A: Using trigonometric  formulas

Q: Find the angle θ (in radians and degrees) between 3x + y = 6 and 5x − 2y = −4.

A: Our Aim is to find the angle (θ) in radians and degress between 3x+y=6 -(i) and 5x-2y=-4 -(ii)

Q: A rectangular box has length 11 inches, width 20 inches, and a height of 7 inches. Find the angle…

A:

Q: Find the angle between v and w to the nearest degree.

A: SOLUTION-

Q: The angle between 0 and 2T in radians that is coterminal 55 T in radians is 8 with the angle

A:

Q: The shadow of a red-pine tree in Northern Minnesota is 131 feet long when the angle of depression…

A: Given: The red-pine tree AB with its shadow BC = 131 ft. The angle of depression is 31o.

Q: A 20-ft ladder leans against a building so that the angle between the ground and the ladder is 72…

A:

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

A:

Q: Find the angle θ, in radians, in the given right triangle. The length of the side adjacent to θ is…

A: Given, the side adjacent to θ = 19 the length of the side opposite θ = 15

Q: Find the angle between v = -3i + 2j and w = 4i - j.Round to the nearest tenth of a degree.

A:

Q: Find the angle 0 between v = cos 60°i+ sin 60°j and w = cos 135°i+ sin 135°j. If necessary, round to…

A: Find the angle between two vectors

Q: A rectangular box has length 5 inches, width 18 inches, and a height of 13 inches. Find the angle…

A:

Q: A 15-ft ladder leans against a building so that the angle between the ground and the ladder is 74…

A: Let AB represent the building and AC represent the ladder. So the triangle formed by the ladder,…

Q: player is

A:

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: A radio tower is located 425 feet from a building. From a window in the building, a person…

A: Given that, a radio tower is located 425 feet from a building and the angle of elevation to the top…

Q: A 20 ft ladder leans against a building so that the angle between the ground and the ladder is 81…

A: A 20 ft ladder leans against a building so that the angle between the ground and the ladder is 81…

Q: The rear wheel of a tractor has a 23​-in radius. Find the angle​ (in​ radians) through which a wheel…

A: The radius of the wheel is 23 in, the time taken to rotate the wheel is 13 sec and the speed of the…

Q: A radio tower is located 300 feet from a building. From a window In The building, a person…

A: Answer is in below step

Q: The angle between 0 and 2T in radians that is coterminal with the angle T in radians is 2

A:

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

A:

Q: In the figure, a person standing at point A notices that the angle of elevation to the top of the…

A: 1°=60'Therefore, 48°30'=48.5°44°10'=44.167°

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

A:

Q: One leg of a right triangle is 4 feet long, and the angle next to it is π/5 radians. Find the length…

A: We have to find

Q: a person is standing on the roof of a building and is 34 feet away from the base of the building.…

A: The angles and the sides of a right triangle are related by using trigonometric functions.…

Q: The angle between 0 and 2T in radians that is coterminal 62 T in radians is 9 with the angle

A: To get coterminal angles, we have to add or subtract 2π.

Q: A 32-ft ladder leans against a building so that the angle between the ground and the ladder is 79…

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.