CORREL 1 MATH Questionnaires (Trigonometry and Analytic Geometry)
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-- A Quonset hut 18 meters long has a parabolic cross section. Its base is 16.1 meters wide and its height at the center is 12.4 meters. A flat horizontal ceiling 12.2 meters wide is constructed inside the hut. How high is the ceiling above the base?
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-- A flagpole stands on top of a pedestal. From a point O at the same elevation as the base of the pedestal, the vertical angle of the top of the flagpole is 60° and the vertical angle of the bottom of the flagpole is 52°. Point O is 14.8 m. away from the base of the pedestal. How long is the flagpole in meters?
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-- A line passing through (5,3) has a slope of 3/2. Find the distance, measured along the line, from the point (5,3) to the y-axis.
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-- An observer measured the angle of elevation of a building from X on a level ground as 32°. Moving 100 m. closer to the building, the angle of elevation was 47°. Find the height of the building.
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-- An observer measured the angle of elevation of a mountain from a point on a level ground as 8.23°. Moving 450 m. closer to the mountain, the angle of elevation is 9.44°. All points are on the same vertical plane. What is the height of the mountain?
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-- An observer wishes to determine the height of the tower. He observed the top of the tower from A and got an angle of elevation of 30°. He then walked 25 m. closer to point B and observed the angle of elevation as 40°. Point A and B are at the same elevation, and on a direct line with the tower. How high is the tower?
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-- Find the distance between the foci of the curve 9x^2 + 25y^2 - 18x + 100y - 116 = 0.
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-- Find the length of the latus rectum of the parabola x2 - 6x = 12y+ 51.
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-- From the point A, 20 m. above point B, the angle of elevation of the top of the tower is 29.33°. From the point B on the ground, 150 m. horizontally from A, the angle of elevation of the top of the tower is 63.56°. What is the height of the tower? Point A has an elevation of 85.45 m.
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-- From the third-floor window, 9 m. above the ground, an observer measured the angle of elevation of the top of a nearby building to be 68° and the angle of depression of its base to be 8°. What is the height of the building?
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-- Given the hyperbola x2 - 8x - 4y2 - 16y = 256. What is the distance between foci?
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-- Line A has a slope of -4 and passes through (-25, -10). Line B has x-intercept of 10 and y-intercept of 25. Determine the point of intersection of lines A and B.
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-- The perimeter of an ellipse is 28.448 units. If the major axis is 10 units, what is the length of the minor axis?
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-- Two sides of a triangle measure 18 cm and 6 cm. The third side may be:
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-- What is the distance from the line 2x -y + 10 = 0 to the center of the graph of the equation x^2 + y^2 - 6x + 12y + 9 = 9?
60.98 m
A cooling tower is a hyperbolic structure. Suppose its base diameter is 100 meters and its smallest diameter of 48 meters occurs 84 meters from the base. If the tower is 120 meters high, approximate its diameter at the top.
4
A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and depth 1 inch. How far from the center of the mirror will the incoming light collect?
20.86 miles N70*21'W
A ship sails 15.0 mi on a course S40°10'W and then 21.0 mi on a course N28°20'W. Find the distance and direction of the last position from the first.
AC = 73
A surveyor can measure the width of a river by setting up a transit at a point C on one side of the river and taking a sighting of a point A on the other side. After turning through an angle of 90° at C, the surveyor walks a distance of 200 meters to point B. Using the transit at B, the angle is measured and found to be 20°. What is the width of the river rounded to the nearest meter?
x = 21.21 miles
A tour boat travels 10 miles due north from its starting point and then travels in the direction S40°W on its second leg of the tour. If the boat is currently 15 miles from its starting point, how far has it traveled on the second leg?
z = 2.64
A tree growing on hillside casts 10.2 meters shadow straight downhill. Find the vertical height of the tree if, relative to the horizontal, the hill slopes 15° and the angle of elevation of the sun is 62°.
96 m
An arch 18 m high has the form of parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64m. Find the width of the arch at the bottom.
h = 130.62'
An observer measures an angle of elevation of 41° for the top of a lighthouse with respect to a certain point on the ground. She then walks 15 feet closer to the lighthouse and measures an angle of elevation of 44°. How tall is the lighthouse?
minimum distance = 77.19x10^6 maximum distance = 108.81x10^6
Assume that the length of the major axis of Earth's orbit is 186,000,000 miles and that the eccentricity is 0.017. Approximate, to the nearest 1000 miles, the maximum and minimum distances between Earth and the sun.
32.57 degrees
Determine the acute angle between the lines 4x - 3y +9 = 0 and 3x - 8y + 1 = 0.
C (2, -3) r = 6 units
Determine the center and radius of the circle with equation x2 + y2 - 4x + 6y - 23 = 0
d = 7.16 units
Determine the distance from the point (5, -3) to the line 2x - 4y + 10 = 0
9y + x - 22 = 0
Determine the equation of the line passing through the points (-5, 3) and (4, 2)
Parallel: 4y -x + 22 = 0 Perpendicular: y + 4x - 3 = 0
Find the equation of the line parallel and perpendicular to x - 4y = 3 and passing through the point (2,-5).
h = 56.39 m
From a building across, the angle of depression of the base of the front edifice is 23.5° and the angle of elevation to the top is 52.78°. The height of observation is 14 m. What is the height of edifice?
h = 24.94 m
The arch of a bridge is on the shape of a semi-ellipse having a horizontal span of 90 m and a height of 30 m at its center. How high is the arch 25 m to the right or left of the center?
a = 12? 0 triangles formed a = 17? 2 triangles formed a = 23? 1 triangle formed
Triangle ABC has the following data: b=19 and A=50°. How many triangles may be formed if a = 12? a = 17? a = 23?
x = 69.46 miles
Two motorboats start from the same point. One of them travels in the direction N30 W at 45 miles per hour, and the other heads due east at 35 miles per hour. How far apart are the boats after 1 hour?
d = 20 m
Two surveyors need to find the distance across a lake. They place a reference pole at point A in the diagram. Point B is 3 m. east and 1 m. north of the reference point A. Point C is 19 m. east and 13 m. north of point A. Find the distance across the lake, from B to C.