Question

Surveying To find the distance $d$ between two points $P$ and $Q$ on opposite shores of a lake, a surveyor locates a point $R$ that is 50.0 meters from $P$ such that $R P$ is perpendicular to $P Q,$ as shown in the figure. Next, using a transit, the surveyor measures angle $P R Q$ as $72^{\circ} 40^{\prime} .$ Find $d$ (FIGURE CANNOT COPY)

Name: Problem 29, Chapter 5: Precalculus: Functions and Graphs
Uploaded: 2021-05-23T06:16:08-08:00
Duration: 1 min 55 s
Channel: Manisha Sarker
Description: Surveying To find the distance d between two points P and Q on opposite shores of a lake, a surveyor locates a point R that is 50.0 meters from P such that R P is perpendicular to P Q, as shown in the figure. Next, using a transit, the surveyor measures angle P R Q as 72^∘ 40^' . Find d (FIGURE CANNOT COPY)

   Surveying To find the distance $d$ between two points $P$ and $Q$ on opposite shores of a lake, a surveyor locates a point $R$ that is 50.0 meters from $P$ such that $R P$ is perpendicular to $P Q,$ as shown in the figure. Next, using a transit, the surveyor measures angle $P R Q$ as $72^{\circ} 40^{\prime} .$ Find $d$ (FIGURE CANNOT COPY)

Precalculus: Functions and Graphs

Earl W. Swokowski,… 12th Edition

Chapter 5, Problem 29

Instant Answer

Solved by Expert Manisha Sarker

05/23/2021

Step 1

We have a right triangle PRQ, where PR is perpendicular to PQ. The length of PR is given as 50 meters. The angle PRQ is given as 72 degrees and 40 minutes. We need to find the length of PQ, which we denote as $d$. Show more…

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Surveying To find the distance $d$ between two points $P$ and $Q$ on opposite shores of a lake, a surveyor locates a point $R$ that is 50.0 meters from $P$ such that $R P$ is perpendicular to $P Q,$ as shown in the figure. Next, using a transit, the surveyor measures angle $P R Q$ as $72^{\circ} 40^{\prime} .$ Find $d$ (FIGURE CANNOT COPY)

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Key Concepts

Surveying Techniques

Surveying is the process of measuring and mapping out positions, distances, and angles on the Earth's surface. It often relies on indirect methods such as triangulation, where intermediate points and angles are used to determine distances that are difficult to measure directly.

Right Triangle Trigonometry

Right triangle trigonometry is the study of the relationships between the angles and sides of triangles with one 90-degree angle. It is essential for solving problems where a right angle provides a natural reference for applying specific trigonometric ratios to calculate unknown distances.

Tangent Function in Trigonometry

The tangent function relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the adjacent side. It is particularly useful in techniques like triangulation in surveying, where it allows one to compute unknown distances when an angle and one side length are known.

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