On Discovering Myself J B Serrano and M G Lapid

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  • Topic: Length, Lighthouse, Inch
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UNIVERSITY OF CALOOCAN CITY
CAMARIN CAMPUS
TULIP ST. CAMARIN CALOOCAN CITY

Title.
Application of solutions of a right triangle in partial fullfilment the requirements in plane trigonometry.

Submitted by:
BSIS 1-A Grp # 4
1. Villanueva, Ruth D.
2. Lupiba, Gretchen
3. De Asis, Ramilyn
4. Balais, Mark Gil
5. Tenorio, Emil
6. Calzada, Janille

Submitted to:
Mr. Varilla
Date of Submission:
January 29, 2011

7. The angle elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30° find the HEIGHT of the tree?

Tan Ɵ a/b
Let a= be the height of the tree, so
That tan Ɵ =a/b therefore we have
Tan 30° a/25 ft
a=25 ft (tan 30°)
a=25 ft (0.5774)
a=14.43 ft
The height of the tree is approximately 14.43 ft.

8. A tree casts a shadow that is 20 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66° determine the HEIGHT of the tree.

Tan Ɵ a/b
Let a= be the height of the tree .So
That tan Ɵ =a/b therefore we have
tan 66° a/20 ft
a=20 ft (tan 66°)
a=20 ft (2.2460)
a=44.92 ft
The height of the tree is approximately 44.92 ft.

14. A man standing 230 ft. form the foot of a church spire finds that the angle of elevation of the top is 63.75°. if his eye is 5 ft 10 inches above the ground what is the height of the spire?

Tan Ɵ a/b
Let a= be the height of the spire
5ft.10 inches= 5.83ft.
Tan Ɵ =a/b therefore we have
Tan 63.75° a/230 ft
a=5.83 ft + 230ft. (tan 63.75°)
a=5.83 ft + 230 ft. (2.0278)
a=5.83 ft + 466.39 ft.
a=472.23ft.
the height of the spire is approximately 472.23 ft.

2. Ron and Francine are building a ramp for performing skateboard stunts. The ramp is 7 feet long and 3 ft high. What is the ANGLE OF ELEVATION that the ramp makes the ground?

Sin Ɵ= a/c
Let Ɵ = be the angle of the elevation. so
Sin Ɵ =a/c therefore, we have
Sin Ɵ =3 ft./ 7 ft
Sin Ɵ = 0.4286
Ɵ = 25.38°
the angle of elevation that the ramp makes with the ground is approximately 25.38°

2. From the top of a tower, the angle of depression of a person is 56°. If the distance from the person to base of the tower is 180 meters, how high is the tower?

Cot Ɵ= b/a
Let a = be the height of the tower. So,
Cot Ɵ =b/a therefore, we have
Cot 56°= 180/a
1.4826 a= 180 m/a
1.4826 a= 180 m
1.4826 a /1.4826 = 180 m/ 1.4826
A=121.41 meters
The height of the tower is approximately 121.41 meters.

2. from the top of a lighthouse, 120 m. above the sea, the angle of depression of a boat is 15”, how far is the boat from the lighthouse?

Tan Ɵ a/b
Let b= be the distance between the boat from the lighthouse. So, tan Ɵ =a/b therefore we have
Tan 15°= 120/b
2-√3= 120/b
2-√3b= 120m
2√3b/2-√3= 120m/2-√3
B= 120m. / 2-√3
B= 447.85 m.
the boat in approximately 447.85 m. far from the lighthouse.

4. A man from the roof of a building 20 m. high finds that the angle of depression of an automobile on the road is 75°10’. How FAR is the automobile from the base of the building?

Cot Ɵ= b/a
let b = be the distance between the automobile from the base of the building. So, Cot Ɵ =b/a therefore, we have
Cot 75°10’= b/20m.
B= 20m (cot 75°10’)
B=20m (3.7760)
B= 75.52 m
The automobile is approximately 75.52m. Far from the base of the building.

6. from the top of a cliff which rises vertically 168.5 ft. above a river bank, the angle of depression of the opposite bank is 53°10’20”. How WIDE is the river?

Cot Ɵ= b/a
Let b = the wide of the river. So,
Cot Ɵ =b/a therefore, we have
Cot 53°10’20”= b/168.5 ft.
B= 168.5 ft (cot 53°10’20”)
B=168.5 ft (1.3354)
B= 225.01 ft
The river is approximately 225.01 ft wide .
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