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Trigonometry Word Problems

Majority of the students do not attempt word problems (height an distances) from trigonometry in papers as they find them hard and they leave those questions unattempted. However, if the students are well versed with the basics of height and distances then they will find trigonometry word problems extremely easy. Let us consider some basics of height and distances before solving the problems.

What is Angle of Elevation?
The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal, when the point being viewed is above the horizontal level. What is Angle of Depression?
When the line of sight is below the horizontal level, the angle so formed by the line of sight with the horizontal, is called the angle of depression. Points to Remember:
1)
Angle of elevation and depression ae always acute angles.
2) Unless stated, it is assumed that the height of the observer is not considered.

Trigonometric Identities
Here we are discussing some shortcuts tips and tricks for our students so that next time you are in a position to solve complex questions within seconds.

Q29) The angle of elevation of the tip of the tower from a point on the ground is 45°. Moving 21 m directly towards the base of the tower, the angle of elevation changes to 60°, then what is the height of the tower, to the nearest metre?

1)
48 m
2) 49 m
3) 50 m
4) 51 m

Solution:
Hence, option 3.

Directions for Questions 30 to 32.

As seen from the top and bottom of a building of height h m, the angles of elevation of the top of a tower of height are α and β respectively.

Q30) If β = 30°, then what is the value of tan α ?

1)
1/2
2) 1/3
3) 1/4
4) 1/5

Solution:
Hence, option 2.

Q31) If α = 30°, then what is the value of tan β ?

1)
1
2) 1/2
3) 1/3
4) 1/4

Solution:
Hence, option 1.

Q32) If α = 30° and h = 30 m, then what is the distance (in m) between the base of the building and the base of the tower?

1)
15 + 15 sqrt(3)
2) 30 + 15 sqrt(3)
3) 45 + 15 sqrt(3)
4) 60 + 15 sqrt(3)

Solution:
Hence, option 3.

Q33) If the angle of elevation of a tower from two distant points a and b (a > b) from its foot and in the same straight line and on the same side of it are 30° and 60° then the height of the tower is Solution:

Hence, option 1.

Q34) A man standing in one corner of a square football field observes that the angle subtended by the pole in the corner just diagonally opposite to this corner is 60°. When he retires 80 m from the corner, along the same straight line, he finds the angle is 30°. The length of the field is

1)
20 m
2) 40√2 m
3) 20√2 m
4) 40 m

Solution:
Hence, option 4.

Q35) At the foot of a mountain, the elevation of its summit is 45°. After ascending 2 km towards the mountain upon an incline of 30°, the elevation changes to 60°. The height of the mountain is Solution:

Hence, option 1.

Q36) A spherical balloon of radius r subtends an angle of 60° at the eye of an observer. If the angle of elevation of its center is 60° and h is the height of the center of the balloon, then which one of the following is correct? Solution:

Hence, option 2.