Question

find the missing sides. leave all answers that are not integers in radical form. (5 pts. each)

1. the bottom of a ladder is placed 12 m away from the wall. the bottom of the ladder is then moved so that the angle made by the wall and ladder is 60°. how far above the ground is the top of the ladder? (hints: of meets the way) draw and label a picture for full credit. (6 pts)

6.
7.
8.
9.

Explanation:

Problem 5

Step1: Define given values

Let $x$ = height of ladder on wall, adjacent side = $12$ m, $\theta=30^\circ$

Step2: Use tangent function

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(30^\circ)=\frac{x}{12}$

Step3: Solve for $x$

$x=12\times\tan(30^\circ)=12\times\frac{\sqrt{3}}{3}$

Step1: Apply Pythagorean theorem

$JG^2 + (\sqrt{6})^2 = 16^2$

Step2: Simplify and solve for $JG$

$JG^2 + 6 = 256$
$JG^2=256-6=250$
$JG=\sqrt{250}=5\sqrt{10}$

Step1: Apply Pythagorean theorem

$6^2 + x^2 = 12^2$

Step2: Simplify and solve for $x$

$36 + x^2 = 144$
$x^2=144-36=108$
$x=\sqrt{108}=6\sqrt{3}$

Answer:

$4\sqrt{3}$ m

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Problem (Top Left, $JG$)