**Trigonometry Angles of Elevation and Depression Questions : **

Here we are going to see some practice questions involving angles of elevation and depression.

**Question 17 :**

From the top and foot of a 40 m high tower, the angles of elevation of the top of a lighthouse are found to be 30° and 60° respectively. Find the height of the lighthouse. Also find the distance of the top of the lighthouse from the foot of the tower.

**Solution :**

AB = x m and BD = 40 m

In triangle ABC :

∠ACB = 30°

tan θ = opposite side/Adjacent side

tan 30° = AB/BC

1/√3 = x/BC

BC = x√3 ----(1)

In triangle ADE :

∠AED = 60°

tan θ = opposite side/Adjacent side

tan 60° = AD/DE

√3 = (x + 40)/DE

DE = (x + 40)/√3 ---->(2)

(1) = (2)

x√3 = (x + 40)/√3

3 x = x + 40

3x - x = 40

2x = 40

x = 20

Height of the tower = 40 + 20 = 60 m

**Question 18 :**

The angle of elevation of a hovering helicopter as seen from a point 45 m above a lake is 30° and the angle of depression of its reflection in the lake, as seen from the same point and at the same time, is 60°. Find the distance of the helicopter from the surface of the lake.

**Solution :**

From the given information, we can draw a rough diagram

In a right triangle FAE :

tan θ = opposite side/Adjacent side

tan 30° = FE/AE

1/√3 = (h-45)/AE

AE = (h - 45) √3 ----(1)

In right triangle ACE :

tan θ = opposite side/Adjacent side

tan 60° = EC/AE

√3 = (ED+DC)/AE

√3 = (45+h)/AE

AE = (45 + h)/√3----(2)

(1) = (2) (BC = AD)

(h - 45) √3 = (45 + h)/√3

3(h - 45) = 45 + h

3h - 135 = 45 + h

2h = 45 + 135

2h = 180

h = 90

Hence the distance of the helicopter from the surface of the lake is 90 m.

After having gone through the stuff given above, we hope that the students would have understood the concept of solving trigonometry angles of elevation and depression.

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