A surveyor measured the angle of elevation of a flat spire as 15⁰ from a point on horizontal ground. He moves 30m nearer to the flat and measures the angle of elevation as 43⁰ . Calculate the height of the spire to the nearest hundredth.

Q: A 200-foot cliff drops vertically into the ocean. If the angle of elevation from a ship to the top…

A: Let the distance of the ship offshore is x feet. A rough sketch of given situation is shown below…

Q: An air traffic controller on top of a 300-foot airport tower looks up and sees a balloon. The angle…

A: An air traffic controller on top of a 300-foot airport tower looks up and sees a ballon.The angle of…

Q: Two buildings of equal height are 800 feet apart. An observer on the street between the buildings…

A:

Q: On a particular day, the distance of the Earth to the sun was 9.2x107 mi. and the distance from Mars…

A:

Q: A person standing 251 feet from the base of a church observed the angle of elevation to the church's…

A:

Q: What is the measure of the angle complementary to 12 degrees

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Q: An airplane is flying 5000 feet above the ground. If the angle of depression to the airport runway…

A: Use tan theta to calculate ground distance

Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and…

A: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and…

Q: The Statue of Liberty is approximately 305 feet tall. If the angle of elevation from a ship to the…

A:

Q: Calculate the unknown angles.

A: Note : As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: A ranger at the top of a fire tower observes the angle of depression to a fire on level ground to be…

A: From the given problem the representative diagram is as shown below.

Q: A 20-foot support post leans against a wall, making a 70° angle with the ground. To the *nearest…

A: sin theta=opposite/hypotenuse

Q: the acute angle (in radians) between the two straight lines y=3x +2 and y=4x+7 is closest to what…

A:

Q: A hiker at the top of a 462-ft mountain measures the angle of depression from the top of a mountain…

A: NOTE: Refresh your page if you can't see any equations. . here we have AB=462 C=5 BC=x

Q: The Seattle Space Needle casts a 67-meter shadow. If the angle of elevation from the tip of the…

A: Given: The angle of elevation from the tip of the 67-m shadow to the top of the Space Needle is 70°.

Q: A tower casts a shadow that is 154 feet long when the angle of elevation to the sun is 52°. How tall…

A: We use the definition of tan of an angle heretanθ =opposite sideadjacent side

Q: An 18 - foot high lamppost casts a shadow. If the angle of elevation from the tip of the shadow to…

A:

Q: simon is due north of a tall totem pole and walks 75m, 40° west of south. From his new position, the…

A:

Q: To estimate the height of a mountain above a level plain, the angle of elevation to the top of the…

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Q: A person standing 188 ft from the base of a church observed the angle of elevation to the church's…

A: Given:  The person standing 133 ft from the base of church observed the angle of elevation to the…

Q: A forest ranger views a tree that is 200 feetaway with a viewing angle of 20°. How tall is the tree…

A: Given Information -  The forest ranger is 200 feet away from the tree. The viewing angle is 20° to…

Q: A person standing 376 feet from the base of a church observed the angle of elevation to the church's…

A:

Q: From the top of a lighthouse 45 meters above sea level, a swimmer is observed swimming with angle of…

A: The diagram for given situation will be    whre AB=45m hieght of light houseC, position of…

Q: The angle of elevation from a boat to the top of a 92-meter hill is 12. How far is the boat from the…

A: The angle of elevation from a boat.

Q: A boy is singing Lupang Hinirang at a location in which the angle of elevation of the top of a 4-m…

A: A boy is singing Lupang Hinirang at a location in which the angle of elevation of the top of a 4-m…

Q: 53

A: Here we find the missing angle.

Q: A person standing 388 feet from the base of a church observed the angle of elevation to the church's…

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Q: A geologist measured the angle of elevation to the top of a mountain to be 39°. From a point 200…

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Q: The most powerful lighthouse on Lake Michigan is 50 m tall. Suppose you are in a boat just off the…

A:

Q: From a point on level ground 125 feet from the base of a tower, the angle ofelevation is 57.2°.…

A: let a represents the height of the tower. In the right triangle, we have a known angle, an unknown…

Q: From the top of a 213-ft lighthouse, the angle of depression to a shop in the ocean is 17°.  How far…

A:

Q: The leaning tower of Pisa in Italy is 55.9 m tall and is leaned at an angle of 86˚ with the ground.…

A:

Q: A radio tower is located 350 feet from a building. From a window in the building, a person…

A:

Q: If the shadow cast by a 600 feet tall tree is 1648.48 feet, find the angle (to the nearest tenth of…

A: Let AB represents the tree and BC represents the shadow, Then angle C is the angle of elevation of…

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: Find the measure of the bolded angle.

A: The measure of the bolded angle  8x + 14 can be calculated using the property of vertical opposite…

Q: Find the measure of the indicated angle.

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Q: The angle of elevation to the top of Wayne Tower in Gotham City is found to be 14° from the ground…

A:

Q: A surveyor measured the angle of elevation of a flat spire as 15° from a point on horizontal ground.…

A: Let the height of the spire is the measurement of a line segment which is normal to the horizontal…

Q: The altimeter of a jet airplane approaching Eusebio International Airport records 6,300 feet as it…

A:

Q: The angle of depression of a submarine from another ship is 28 degrees. The submarine is 791 feet…

A:

Q: A radio transmission tower is 180 feet high. How long should a guy wire be if it is to be attached…

A:

Q: What is the measurement, in degrees, of the reference angle to an angle measuring 312°?

A:

Q: A forester standing 200 feet from the base of a redwood tree observes that the angle of…

A:

Q: A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level, and…

A: Let the angle of elevation be 'θ' and the length of the string be 'x'. Let the height of the kite…

Q: A 4-m beam is used to brace a wall. If the bottom of the beam is 3 m from the base of the wall, what…

A: Since a 4 m beam is used to brace a wall and given that if the bottom of the beam is 3 m from the…

Q: A surveyor measures the lengths of a triangular plot of land as 420 feet, 350 feet and 180 feet.…

A: We sketch the triangle roughly  We have to find C

Q: From a point on the ground 100 m from the foot of a cliff, the angle ofelevation of the top of the…

A: Given that from a point on the ground 100m from the foot of a cliff, the angle ofelevation of the…

Q: A sprinkler on a golf course fairway is set to spray water over a distance of 70 feet and rotates…

A: Given, sprinkler rotates through an angle 48o and sprays water over a distance of 70 feet.

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.