Question

question 5: standard g.srt.8
solve for the missing side using the pythagorean theorem.
right triangle with leg 5, hypotenuse 13, and leg ?
a. 12
b. 24
c. 25
d. 10
question 6: standard g.srt.8
solve for the missing side using the pythagorean theorem.
right triangle with hypotenuse 20, leg 10, and leg ?
a. 5
b. 17.3
c. 13.5
d. 22.2
question 7: standard g.srt.8
solve for the missing side using the pythagorean theorem.
right triangle with leg 5, leg 14, and hypotenuse ?
a. 12
b. 4.8
c. 14.8
d. 16.9

Explanation:

Question 5

Step1: Recall Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let the missing side be \(x\), one leg \(a = 5\), hypotenuse \(c=13\). We need to find the other leg \(x\). So we can rewrite the formula as \(x^{2}=c^{2}-a^{2}\)

Step2: Substitute values

Substitute \(a = 5\) and \(c = 13\) into the formula: \(x^{2}=13^{2}-5^{2}\)
Calculate \(13^{2}=169\) and \(5^{2} = 25\), then \(x^{2}=169 - 25=144\)

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{144} = 12\)

Step1: Recall Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\). Let the missing side be \(x\), one leg \(b = 10\), hypotenuse \(c = 20\). We find the other leg \(x\) using \(x^{2}=c^{2}-b^{2}\)

Step2: Substitute values

Substitute \(b = 10\) and \(c=20\) into the formula: \(x^{2}=20^{2}-10^{2}\)
Calculate \(20^{2}=400\) and \(10^{2}=100\), then \(x^{2}=400 - 100 = 300\)

Step3: Solve for \(x\)

Take the square root of 300: \(x=\sqrt{300}\approx17.3\) (since \(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\approx17.32\))

Step1: Recall Pythagorean theorem

For a right triangle, \(a^{2}+b^{2}=c^{2}\). Let the missing side (hypotenuse) be \(x\), one leg \(a = 5\), another leg \(b=14\). We use \(x^{2}=a^{2}+b^{2}\)

Step2: Substitute values

Substitute \(a = 5\) and \(b = 14\) into the formula: \(x^{2}=5^{2}+14^{2}\)
Calculate \(5^{2}=25\) and \(14^{2}=196\), then \(x^{2}=25 + 196=221\)

Step3: Solve for \(x\)

Take the square root of 221: \(x=\sqrt{221}\approx14.8\) (since \(\sqrt{221}\approx14.83\))

Answer:

a. 12

Question 6