 Krishna
0

Step 1:  Examine the given information in the question.

NOTE:  Height of the building = 6 m

An angle of depression from the top of the building to the target = 60\degree

The distance between the shooter(me) and the object = ?

Step 2:  Draw a figure by using the given measurements.

• Step 1:  Make a perpendicular line of length 6 m and assume it is a building
• Step 2:  From the top of the perpendicular line assume an horizontal line. Angle of depression 60 \degree is considered with reference to horizontal line.
• Step 3: Draw a line from the top of the building to the target with an angle of depression. Step 3: Use the trigonometric ratios to find unknown length.

NOTE:  To find the hypotenuse we need to take the sine because we know opposite side of the angle.

From the figure:

\sin \theta = \frac{opposite}{hypotenuse} = \frac{AB}{AC}

\sin 60\degree = \frac{6}{BC}     ( \because PB and AC are parallel line,   \angle PBC = \angle BCA because they are alternating interior angles)

\frac{\sqrt{3}}{2} = \frac{6}{BC} ( \because \sin 60\degree = \frac{\sqrt{3}}{2})

BC = \frac{2*6}{\sqrt{3}}

BC = \frac{2*2*(\sqrt{3})^2}{\sqrt{3}}

BC=4\sqrt{3}m

The distance between the shooter(me) and the object = BC=4\sqrt{3}\ m