Question

1. find the perimeter of the triangle:triangle image with side lengths 8, 8, 8, height $4\sqrt{15}$, and 60° angles marked22. find the perimeter of the square:square image with diagonal length 28 marked23. steel loading ramps are used to load a lawn mower onto a truckbed 37.5 inches above the ground. if the ramps make a 30° angle with the ground, find the length of the ramps in feet.24. the infield of a baseball field is a square with sides measuring 90 feet. a ball thrown from third to first base is caught in 1.2 seconds. find the speed of the ball in feet per second. round to the nearest tenth.

Explanation:

Problem 21

Step1: Identify side lengths

The triangle has three sides: $8$, $8$, $8$.

Step2: Calculate perimeter

Perimeter = sum of all sides
$P = 8 + 8 + 8$

Step1: Relate diagonal to side

For a square with side $s$, diagonal $d = s\sqrt{2}$. Given $d=28$, solve for $s$.
$s = \frac{28}{\sqrt{2}} = 14\sqrt{2}$

Step2: Calculate perimeter

Perimeter of square = $4s$
$P = 4 \times 14\sqrt{2} = 56\sqrt{2}$

Step1: Convert height to feet

Truckbed height: $37.5$ inches = $\frac{37.5}{12} = 3.125$ feet

Step2: Use sine for ramp length

For $30^\circ$ angle, $\sin(30^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\text{height}}{\text{ramp length}}$. Since $\sin(30^\circ) = 0.5$,
$\text{Ramp length} = \frac{3.125}{0.5}$

Answer:

$24$

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Problem 22