## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 8 - Right Triangles and Trigonometry - 8-4 Angles of Elevation and Depression - Practice and Problem-Solving Exercises - Page 520: 25

#### Answer

Both the angle of elevation and the angle of depression are $72^{\circ}$.

#### Work Step by Step

For this exercise, the angle of elevation and the angle of depression are the same because they are actually alternate interior angles, and alternate interior angles are congruent to one another. Let's set the angle of elevation $e$ equal to the angle of depression $d$: $7x - 5 = 4(x + 7)$ Distribute on the right side of the equation: $7x - 5 = 4x + 28$ Subtract $4x$ from each side of the equation to move variables to the left side of the equation: $3x - 5 = 28$ Add $5$ to each side of the equation to move constants to the right side of the equation: $3x = 33$ Divide each side by $3$ to solve for $x$: $x = 11$ We are asked to find $e$ and $d$. Let's set up the expression to find $e$: $e = 7x - 5$ Plug in $11$ for $x$: $e = 7(11) - 5$ Multiply first, according to order of operations: $e = 77 - 5$ Subtract to solve for $e$: $e = 72^{\circ}$ Let's set up the expression to find $d$: $d = 4(x + 7)$ Substitute $11$ for $x$: $d = 4(11 + 7)$ Evaluate what is in parentheses first: $d = 4(18)$ Multiply to solve for $d$: $d = 72^{\circ}$

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