1.) You were on top of a coconut tree that is 4m from the ground when you saw your friend and your brother coming from the same direction at angles of depression of 28 degree and 35 degree, respectively. What is your direct distance from them? Who is farther? your friend or your brother? How far are they from each other?
Solution:
ΔABC
tan ϴ = opposite/adjacent
tan ϴ = AB/BC
tan 35° = 4/BC
BC(0.70020753821) = 4
BC = 4/0.70020753821
BC = 5.71259202697 m
ΔABD
tan ϴ = AB/BD
tan 28° = 4/BD
BD(0.53170943166) = 4
BD = 4/0.53170943166
BD = 7.52290586141 m
What is your direct distance from them?
You to Brother distance
Using Pythagorean theorem
(AC)² = (AB)² + (BC)²
(AC)² = 4² + 5.71259202697²
(AC)² = 16 + 32.6337076666
(AC)² = 48.6337076666
AC = √48.6337076666
AC = 6.9737871824855682213277657418509 m
You to Friend distance
Using Pythagorean theorem
(AD)² = (AB)² + (BD)²
(AD)² = 4² + 7.52290586141²
(AD)² = 16 + 56.5941125996
(AD)² = 72.5941125996
AD = √72.5941125996
AD = 8.5202178727776674149932602446283 m
Who is farther? your friend or your brother?
The farther is your friend because AD = 8.52 m away from you while your brother is AC = 6.97 m away from you.
How far are they from each other?
CD = BD - BC
CD = 7.52 m - 5.71 m
CD = 1.81 m
2.) Why are diagrams or illustrations important when solving word problems involving right triangles?
Answer:
Diagrams or illustrations are important when solving word problems involving right triangles because it will aid you through the process of solving the problem. It is necessary to draw a diagram because you will easily understand anything that revolves around the problem.
3.) Why is the skill in solving word problems involving right triangles important in real life?
Answer:
The skill in solving word problems involving right triangles is important in real life because everyday, we encounter different kinds of situation. If you have the right skill set, anything that comes along your way can be solve without any difficulty.
4.) How can you develop your skill in solving word problems?
The skill in solving word problems can be develop by practice and by familiarization of the mathematical terms.
Answers & Comments
Problem:
1.) You were on top of a coconut tree that is 4m from the ground when you saw your friend and your brother coming from the same direction at angles of depression of 28 degree and 35 degree, respectively. What is your direct distance from them? Who is farther? your friend or your brother? How far are they from each other?
Solution:
ΔABC
tan ϴ = opposite/adjacent
tan ϴ = AB/BC
tan 35° = 4/BC
BC(0.70020753821) = 4
BC = 4/0.70020753821
BC = 5.71259202697 m
ΔABD
tan ϴ = AB/BD
tan 28° = 4/BD
BD(0.53170943166) = 4
BD = 4/0.53170943166
BD = 7.52290586141 m
What is your direct distance from them?
You to Brother distance
Using Pythagorean theorem
(AC)² = (AB)² + (BC)²
(AC)² = 4² + 5.71259202697²
(AC)² = 16 + 32.6337076666
(AC)² = 48.6337076666
AC = √48.6337076666
AC = 6.9737871824855682213277657418509 m
You to Friend distance
Using Pythagorean theorem
(AD)² = (AB)² + (BD)²
(AD)² = 4² + 7.52290586141²
(AD)² = 16 + 56.5941125996
(AD)² = 72.5941125996
AD = √72.5941125996
AD = 8.5202178727776674149932602446283 m
Who is farther? your friend or your brother?
The farther is your friend because AD = 8.52 m away from you while your brother is AC = 6.97 m away from you.
How far are they from each other?
CD = BD - BC
CD = 7.52 m - 5.71 m
CD = 1.81 m
2.) Why are diagrams or illustrations important when solving word problems involving right triangles?
Answer:
Diagrams or illustrations are important when solving word problems involving right triangles because it will aid you through the process of solving the problem. It is necessary to draw a diagram because you will easily understand anything that revolves around the problem.
3.) Why is the skill in solving word problems involving right triangles important in real life?
Answer:
The skill in solving word problems involving right triangles is important in real life because everyday, we encounter different kinds of situation. If you have the right skill set, anything that comes along your way can be solve without any difficulty.
4.) How can you develop your skill in solving word problems?
The skill in solving word problems can be develop by practice and by familiarization of the mathematical terms.
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