applications of trigonometry - Suppose you are shooting an arrow from the top of a building at a height of 6 m to a target on the ground at an angle of depression of 60\degree.

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

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