You know the lengths of the two legs of a right triangle, and you are trying to solve for the measures of the acute angles of that triangle. Without calculating the length of the hypotenuse, which trigonometric ratio and reciprocal trigonometric ratio would be most useful in this calculation? Why?

Q: This problem requires work. From the top of a vertical cliff 40 m high, the angle of depression of…

A:

Q: A tunnel is planned through a mountain to connect points A and B on two existing roads. If the the…

A:

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: Do all angles have values for all six trigonometric ratios? Why or why not?

A: value of some trigonometric function is undefined  , like tan900,cosec00, sec900,cot00 because…

Q: The radius of a wheel rolling on the ground is 80 centimeters. If the wheel rotates through an angle…

A: Given that the wheel is rotated by an angle of 60°We know that i°=π180 and∴60°=60xπ180rad=π3rad

Q: In a right triangle, the side opposite angle phi has a length of 29.0 meters, the side adjacent to…

A: cot(phi) = base/perpendicular

Q: Solve for the missing side or angle using Trig Ratios (sin, cos, tan) 3. 4.

A:

Q: To the nearest whole number, what angle has a cos ratio of 0.2589? degrees

A: The cos ratio is the cosine value of the angle formed by the ratio of base of a triangle to its…

Q: You know the lengths of the two legs of a right triangle, and you are trying to solve for the…

A: Given lengthsof the two legs of a right triangle are known, and you are trying to solve for the…

Q: How long would a ladder need to be to reach 19 ft high, if it placed so that the base of the ladder…

A: The objective of the question is determine the length of the ladder.

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

A:

Q: If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of…

A: Topic = Circle

Q: If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 23 feet long,…

A:

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: If the central angle is 4π/3 radians, what should the radius of a circle be to make the arc length 2…

A: Given that central angle is 4π/3 radians Arc length =2m To find the radius of a circle

Q: To explain why, for any acute angle u, it is impossible for sec theta =  1/2

A: To show:  It is impossible for sec theta =  1/2

Q: 1. Write a list of angle degree measurements between 0° and 180° whose sin value can most easily be…

A:

Q: what is the angle of elevation of the ladder?  how high does the ladder reach the building ?

A:

Q: If the terminal side of angle θ is in the first quadrant and cos ( θ ) = 1, what is the exact…

A: If the terminal side of angle θ is in the first quadrant and cos ( θ ) = 1,

Q: The bottom of the doorway to a building is 3.01 ft above the​ ground, and a ramp to the door for the…

A: Here we will find the length of the ramp,

Q: ilot flies her plane on a bearing of 35 degrees from point A to point B, which is 400 miles from A.…

A:

Q: If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 18 feet, what…

A: Given Truck height =4 feet Ramp length=18 feet

Q: What is the value of cotθ if the terminal side of angle θ intersects the unit circle in the first…

A: We have to find the value of cotθ if the terminal side of angle θ intersects the unit circle in the…

Q: A guy wire attached to the top of a radio antenna is bolted to the ground 48 m from the base of the…

A:

Q: If the radius of a circle is 4 cm and the arc is 6 cm ... is the angle formed a radian? What is n…

A: The relation between arc length, angle and radius is given as  arc length=radius×angle.

Q: What is the value of csc 0 if the terminal side of angle 0 intersects the unit circle in the first…

A: Given data:     The given value is: x=10⁄17.   The unit circle is the circle having one radius. The…

Q: A straight 33-ft long ladder leans against a building so that the angle between the ground and the…

A:

Q: The angle of elevation from an observer to the top of achurch is 0.3 radian, while the angle of…

A: Firstly Change radian to degree       0.3 radian =17.1887°0.4 radian =22.9183° According to…

Q: If we are given an acute angle and a side in a right triangle, what unknown part of the triangle…

A: If we are given an acute angle and a side in a right triangle, what unknown part of the triangle…

Q: In a right triangle, sin(β) = 0.292. If the hypotenuse of the triangle has a length of 17.5 cm, what…

A:

Q: if side a = 10 is opposite angle A, side b = 4 is opposite B, and side c is the hypotenuse, find the…

A:

Q: In a circle of radius 2, the length of the arc that subtends a central angle of 222 degrees is_____?…

A:

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

A: Please follow the next step.

Q: A tunnel is planned through a mountain to connect points A and B on two existing roads. If the the…

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: In which quadrant is the reference angle unnecessary in finding the values of the trigonometric…

A:

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

Q: In a right triangle, tan 6 0.75. Which side is longer, the opposite or the adjacent side? Explain…

A:

Q: In right triangle ABC, mzC = 90° and AC + BC. Which trigonometric ratio is equivalent to sin B? %3!

A: We know that, for any angle x, sin(90-x)=cosx. Also the sum of the angles of a triangle is 180°.

Q: An acute triangle has an area of 10 square inches. Two sides have lengths 8 inches and 5 inches.…

A:

Q: A circular arc has measure 28 cm and is intercepted by a central angle of 2.9 radians. Find the…

A: Given, arc length=l=28 cm andθ=2.9 radians

Q: The angle of elevation for a ramp is recommended to be 4 degrees. If the horizontal distance from…

A: To find: The length of the ramp. Given information: The angle of elevation for a ramp is recommended…

Q: Find the six trigonometric ratios of each of the acute angles of the given right triangle:

A: Given that:

Q: 2. From a point 20 m from the base of a building, the angle of elevation of the top of the building…

A:

Q: F 45° n=1 N f3=

A: To find:  All six trigonometric angles and sides of triangle.

Q: If sec ? =16/5, what is sin ?? Draw a triangle and give an exact answer. No decimal approximations.

A:

Q: A 36-ft ladder leans against a building so that the angle between the ground and the ladder is 61°.…

A:

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 10 yard rope is strung from the bottom of one tree to the top of another. The angle of elevation…

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.