A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 54 meters from one entrance of the tunnel, at an angle of 56° to the perpendicular. Also according to his equipment, he is 31 meters from the other entrance of the tunnel, at an angle of 13° to the perpendicular. Based on these measurements, find the length of the entire tunnel. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale. meters 56° 54 meters 13 31 meters

Q: 7. A clock has a minutes hand that is 10cm long. In 1 minute, the minutes hand rotates 6 degrees.…

A: The length of the clock hand is r=10 cmThe minute hand rotates θ=6oWe have to find the distance…

Q: An airplane descends at an angle of depression of 22" for a ground distance of 7850 feet. What…

A:

Q: 14. A jet takes off at a 30° angle. The runway (from takeoff) is 875 feet long. Find the altitude of…

A:

Q: Find the smallest angle, in radians to 2 decimal places, in a right-angled triangle with longest…

A: Given right angle triangle so use Pythagoras theorem  to find the third side.. Then  infront of…

Q: A surveyor observes that the angle between the road and the bottom of a bridge girder is 30 degrees.…

A: Given data is : Angle θ=30∘ Bridge clearance is 16.5 feet. To find the horizontal distance from the…

Q: Mo is on a baseball team and hears that a ball thrown at a 44 degree angle from the ground will…

A: Given, Mo is on a baseball team and hears that a ball thrown at a 44 degree angle from the ground…

Q: The shadow of a man is 10 feet long when the angle of elevation of the sun is 30.5°. Determine the…

A:

Q: From the top of an 82 meter high vertical cliff, a boat has an angle of depression of 32 degrees.…

A: We will use trigonometric ratio to solve this.

Q: From Point S, Samantha uses a clinometer to determine the angle of elevation to the top of the cliff…

A:

Q: There is an escalator that is 1083.6 feet long and drops a vertical distance of 196.1 feet. What is…

A:

Q: There are two lifeguard stations along the shoreline. Station B is 50 meters east of station A. A…

A: Given data: The distance between both stations is AB =50 m. The angle made by a swimmer with station…

Q: Tamara wants to calculate the height of a tree outside her home. Using her clinometer, she measures…

A:

Q: You are a secret agent trapped at the top of a tall building. To escape, you decide to slide down a…

A: The objective of this question is to find the length of the zip line. We can use trigonometry to…

Q: When the angle of elevation of the sun is 62 degrees, the shadow east by a vertical pole is 10m…

A:

Q: You are standing on top of a cliff 500 ft. above the ocean looking out at the water.  You see a…

A: tanθ=oppositeadjacentIn this question, opposite is the height and adjacent is the base

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.