Question

Gabriel leans a 18-foot ladder against a wall so that it forms an angle of 73degrees
∘
with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

Answer: 17.21 feet

Step-by-step explanation:

    We will draw a diagram, a picture, to represent the given situation. Let x be how high up the wall this ladder reaches. The ladder is 18 feet long and forms a 73° angle of elevation with the ground. See attached for the diagram I have created.

    Since this forms a right angle (the wall and the ground), we can use trigonometric functions with the right triangle. We are given the hypotenuse (the ladder = 18 feet), an angle (73°), and are finding the opposite side from our angle (height up the wall = x feet). Using this information, we will use the sine property.

    Given:

$\displaystyle sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

    Substitute known values:

$\displaystyle sin(73\°)=\frac{x}{18}$

    Multiply both sides of the equation by 18:

$\displaystyle 18*sin(73\°)=x$

    Evaluate and round to the nearest hundredth:

$\displaystyle x=17.2134856\approx 17.21\;\text{feet}$