Terms related to Application of Trigonometry

• Horizontal level: is a line parallel to ground from eye level of observer.
• Line of sight (LOS): is the line drawn from the eye of an observer to the point in the object viewed by the observer.
• 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, i.e., the case when we raise our head to look at the object.
• Angle of depression: of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e., the case when we lower our head to look at the point being viewed.

Let’s solve one of the questions solved in the Board Exams

Q- If a tower 30 ? high, casts a shadow 10√3 ? long on the ground, then what is the angle of elevation of the sun?

Sol- Height of tower, ℎ=30 ?, Length of shadow =10√3
Let angle of elevation be ?
tan?=30/10√3=√3
⇒tan?=tan60°
⇒?=60°

Q- On a straight line passing through the foot of a tower, two points ? and ? are at distances of 4 ? and 16 ? from the foot respectively. If the angles of elevation from ? and ? of the top of the tower are complementary, then find the height of the tower.

Sol- ℎ/4=tan?          (i)
ℎ/16=tan(90°−?)
⇒ℎ/16=cot?=1/tan?
⇒tan?=16/ℎ             (ii)
From (i) and (ii), we get,
ℎ/4=16/ℎ
⇒ℎXℎ=4×16
⇒ℎ=8 ?
∴ Height of tower =8 ?

Q- An aeroplane is flying at a height of 3000 ? above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use √3=1.732]

Sol- In Δ???,
tan45°=3000/??
⇒??=3000 ?
tan60°=3000/??
⇒??=3000/√3=1000√3 ?
∴ Width of river =??+??=(3000+1000√3) ?

Let’s solve one of the questions: