![2. A tract of land has the shape of a trapezoid, as shown in Figure below. The lengths of
three sides and the sizes of the two interior right angles are given. Determine the two
unknown interior angles and the length of the fourth side.
Figure Q2(a) [73o
18’03”, 106o
41’57”, 104.40m]
Figure Q2(b) [78o
41’24”, 101o
18’36”, 229.46 ft]](https://image.slidesharecdn.com/2tutorial-trigonometry-160704043233/85/S2-1-tutorial-trigonometry-2-320.jpg)
![3. Determine the lengths of the three unknown sides of the tract of land shown in Figure
below.
Figure Q3(a) [AB = 422.62 ft, BC = 875.94 ft, CD = 1032.89 ft]
Figure Q3(b) [BC = 85.828m, CD = 304.08m, DA = 249.99m]](https://image.slidesharecdn.com/2tutorial-trigonometry-160704043233/85/S2-1-tutorial-trigonometry-3-320.jpg)
![4. A triangular parcel of land is bounded on two sides by roads that are perpendicular.
Another highway bounds the third side at an angle of 35o
as shown in figure below. We
are informed that the owner recently fenced the boundary of the property with a total of
1025.5 ft of fencing, but we do not know the lengths of the individual sides. What is the
area of the land in ft2
?
[Area = 43153 ft2
]
5. The vertical angle from level ground to the top of a building 65o
. The angle is measured
from a point that is 100 ft distant from the base of the building. How tall is the building?
[h = 214 ft]
6. A railroad embankment has the shape of a trapezoid, with a horizontal top 25 ft across,
sloping sides each 15 ft in length, and a height of 8 ft. Determine the width at the base of
the embankment.
[Base = 50.38 ft]
7. A triangular piece of land is bounded by 42.5 m of fencing on one side, 51.2 m of stone
wall on another side, and 85.7 m of road frontage on the third side. What are the interior
angles formed by the boundary lines?
[26o
19’14”, 21o
35’43”, 132o
05’03”]
8. To determine the distance between points X and Y on the opposite sides of a river, a
surveyor measures a distance of 300 m between points X and Z, where Z is set on the
same side of the river as X. Angle X-YZ is measured to be 85o
30’ and angle Z-XY is
measured to be 35o
45’. Compute the distance XY.
[XY = 205 m]
9. Two points on the opposite sides of a lake, A and B, are 355.5 and 276.2 ft, respectively,
from a third point, C, on the shore. The lines joining points A and B with point C intersect
at an angle of 81o
15’ (angle C-AB). What is distance AB?
[AB = 415.68 ft]](https://image.slidesharecdn.com/2tutorial-trigonometry-160704043233/85/S2-1-tutorial-trigonometry-4-320.jpg)
S2 1 tutorial trigonometry
- 1. Tutorial 1. Determine the areas of the figures shown below. (a) 198 m2 (b) 450 ft2 (c) 338 m2 (d) 6760 ft2 (e) 2886 m2 (f) 30510 ft2 (a) 165 m2 (b) 1400 ft2 (c) 165 m2 (d) 2864 ft2 (e) 1227 m2 (f) 3474 ft2
- 2. 2. A tract of land has the shape of a trapezoid, as shown in Figure below. The lengths of three sides and the sizes of the two interior right angles are given. Determine the two unknown interior angles and the length of the fourth side. Figure Q2(a) [73o 18’03”, 106o 41’57”, 104.40m] Figure Q2(b) [78o 41’24”, 101o 18’36”, 229.46 ft]
- 3. 3. Determine the lengths of the three unknown sides of the tract of land shown in Figure below. Figure Q3(a) [AB = 422.62 ft, BC = 875.94 ft, CD = 1032.89 ft] Figure Q3(b) [BC = 85.828m, CD = 304.08m, DA = 249.99m]
- 4. 4. A triangular parcel of land is bounded on two sides by roads that are perpendicular. Another highway bounds the third side at an angle of 35o as shown in figure below. We are informed that the owner recently fenced the boundary of the property with a total of 1025.5 ft of fencing, but we do not know the lengths of the individual sides. What is the area of the land in ft2 ? [Area = 43153 ft2 ] 5. The vertical angle from level ground to the top of a building 65o . The angle is measured from a point that is 100 ft distant from the base of the building. How tall is the building? [h = 214 ft] 6. A railroad embankment has the shape of a trapezoid, with a horizontal top 25 ft across, sloping sides each 15 ft in length, and a height of 8 ft. Determine the width at the base of the embankment. [Base = 50.38 ft] 7. A triangular piece of land is bounded by 42.5 m of fencing on one side, 51.2 m of stone wall on another side, and 85.7 m of road frontage on the third side. What are the interior angles formed by the boundary lines? [26o 19’14”, 21o 35’43”, 132o 05’03”] 8. To determine the distance between points X and Y on the opposite sides of a river, a surveyor measures a distance of 300 m between points X and Z, where Z is set on the same side of the river as X. Angle X-YZ is measured to be 85o 30’ and angle Z-XY is measured to be 35o 45’. Compute the distance XY. [XY = 205 m] 9. Two points on the opposite sides of a lake, A and B, are 355.5 and 276.2 ft, respectively, from a third point, C, on the shore. The lines joining points A and B with point C intersect at an angle of 81o 15’ (angle C-AB). What is distance AB? [AB = 415.68 ft]