Question

2.
x = 4√5
4.
6.
loaded furniture into the back of a moving truck...ground, what is the horizontal distance from...

Explanation:

Problem 2:

Step1: Identify triangle type (right triangle)

We have a right triangle with hypotenuse \( c = 21 \) and one leg \( b = 19 \), find the other leg \( x \). Use Pythagorean theorem: \( a^2 + b^2 = c^2 \), so \( x^2 + 19^2 = 21^2 \).

Step2: Solve for \( x^2 \)

\( x^2 = 21^2 - 19^2 = (21 - 19)(21 + 19) = 2 \times 40 = 80 \).

Step3: Find \( x \)

\( x = \sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5} \), which matches the given answer.

Problem 4:

Step1: Identify triangle type (right triangle)

Right triangle with hypotenuse \( c = 12.8 \) and one leg \( b = 5.3 \), find the other leg \( x \). Use Pythagorean theorem: \( x^2 + 5.3^2 = 12.8^2 \).

Step2: Solve for \( x^2 \)

\( x^2 = 12.8^2 - 5.3^2 = (12.8 - 5.3)(12.8 + 5.3) = 7.5 \times 18.1 = 135.75 \).

Step3: Find \( x \)

\( x = \sqrt{135.75} \approx 11.65 \) (rounded to two decimal places).

Problem 6:

Step1: Analyze trapezoid and right triangles

The trapezoid has height \( h = 17 \), non - parallel side (leg of right triangle) \( l = 19 \), and the difference in the lengths of the two bases is split equally between the two right triangles at the sides. Let the base of each right triangle be \( b \).

Step2: Use Pythagorean theorem for right triangle

For the right triangle with hypotenuse \( 19 \) and height \( 17 \), we have \( b^2+17^2 = 19^2 \).

Step3: Solve for \( b \)

\( b^2=19^2 - 17^2=(19 - 17)(19 + 17)=2\times36 = 72 \), so \( b=\sqrt{72}=6\sqrt{2}\approx8.49 \).

Step4: Find the top base \( x \)

The bottom base is \( 31 \), and the sum of the two bases of the right triangles is \( 2b \). So \( x=31 - 2b \). Substituting \( b\approx8.49 \), we get \( x = 31-2\times8.49=31 - 16.98 = 14.02 \) (or using exact values: \( x = 31-2\sqrt{72}=31 - 12\sqrt{2}\approx31 - 16.97 = 14.03 \)).

Answer:

s:

• Problem 2: \( \boldsymbol{x = 4\sqrt{5}} \)
• Problem 4: \( \boldsymbol{x\approx11.65} \) (or exact form \( \sqrt{135.75} \))
• Problem 6: \( \boldsymbol{x\approx14.02} \) (or exact form \( 31 - 12\sqrt{2} \))