Single Right Triangle Models

The Power of Triangles

How do we measure the height of a mountain or the width of a river without a giant ruler? We use trigonometry! By converting real-world scenarios into single right-angled triangles, we can solve for unknown distances using basic angles and ratios.

Problem Statement

Problem. A tower stands vertically on the ground. From a point on the ground, which is $15\text{ m}$ away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60^\circ$. Find the height of the tower.

Given:

• Distance from foot of tower ($BC$) = $15\text{ m}$
• Angle of elevation ($\angle ACB$) = $60^\circ$

Problem Statement

Problem. An electrician has to repair an electric fault on a pole of height $5\text{ m}$. She needs to reach a point $1.3\text{ m}$ below the top of the pole. What should be the length of the ladder inclined at $60^\circ$ to the horizontal? Also, how far from the foot of the pole should she place the ladder? (Take $\sqrt{3} = 1.73$)

Given:

• Total pole height = $5\text{ m}$
• Distance from top to repair point = $1.3\text{ m}$
• Angle of ladder = $60^\circ$

Problem Statement

Problem. An observer $1.5\text{ m}$ tall is $28.5\text{ m}$ away from a chimney. The angle of elevation of the top of the chimney from her eyes is $45^\circ$. What is the height of the chimney?

Given:

• Height of observer = $1.5\text{ m}$
• Distance from chimney ($DE$) = $28.5\text{ m}$
• Angle of elevation = $45^\circ$