Question

7/11 You are attacking an enemy castle. Your strategy is to go over the castle wall. You are 1500 meters away from the bottom of the wall. You measure the angle of elevation to the top of the wall at 30. How tall is the enemy castle wall? 78.6 meters p 1498.0 meters 75.3 meters 78.5 meters

Answer 1

Let the building is represnted by AB and the the man which is attacking on the castle is at O.

as, teh attacker is 1500 meters away from the bottom of the wall

So, OB = 1500 m

Angle of Elevation : The term angle of elevation denotes the angle from the horizontal upward to an objec

the angle of elevation to the top of the wall at 30.

i.e Angle AOB is represented as angle of elevation : Angle AOB = 3°

Thus the figure makes a right angle triangle with 90 degree at angle B

So, In triangle ABO, OB = 1500, and Angle AOB = 3°

we need to find the length of AB

Apply the trignometric ratio of Tangent to the angle AOB

`\tan \theta=(Perpendicular)/(Base)`

Here we have Base = OB and Perpendicular AB and angle = 3

`\begin{gathered} \tan \theta=(Perpendicular)/(Base) \\ \tan 3=(AB)/(OB) \\ \tan 3=(AB)/(1500) \\ AB\text{ = 1500}*\tan 3 \\ AB\text{ =1500}*0.0524 \\ AB=78.6\text{ m} \end{gathered}`

as AB represent the Length of castle

So, The length of castle is 78.6 m

Answer : 78.6 m