Question

question 8 (1 point)
triangle with right angle, one leg 6.5, hypotenuse 9.9, x=____
blank 1:
question 9 (1 point)
triangle with right angle, one leg 3, hypotenuse 6, x=____
blank 1:
question 10 (1 point)
triangle with right angle, one leg 2, hypotenuse 6, x=____

Explanation:

Question 8

Step1: Identify triangle type (right triangle)

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, hypotenuse \(c = 9.9\), one leg \(a = 6.5\), find the other leg \(x\) (let \(b = x\)).

Step2: Rearrange Pythagorean theorem

\(x^2 = c^2 - a^2\)

Step3: Substitute values

\(x^2 = 9.9^2 - 6.5^2\)
\(x^2 = 98.01 - 42.25\)
\(x^2 = 55.76\)

Step4: Take square root

\(x = \sqrt{55.76} \approx 7.47\) (rounded to two decimal places)

Step1: Identify triangle type (right triangle)

Right triangle, use Pythagorean theorem \(a^2 + b^2 = c^2\). Here, hypotenuse \(c = 6\), one leg \(b = 3\), find the other leg \(x\) (let \(a = x\)).

Step2: Rearrange formula

\(x^2 = c^2 - b^2\)

Step3: Substitute values

\(x^2 = 6^2 - 3^2\)
\(x^2 = 36 - 9\)
\(x^2 = 27\)

Step4: Take square root

\(x = \sqrt{27} \approx 5.196\) (or \(3\sqrt{3}\))

Step1: Identify triangle type (right triangle)

Right triangle, use Pythagorean theorem \(a^2 + b^2 = c^2\). Here, hypotenuse \(c = 6\), one leg \(a = 2\), find the other leg \(x\) (let \(b = x\)).

Step2: Rearrange formula

\(x^2 = c^2 - a^2\)

Step3: Substitute values

\(x^2 = 6^2 - 2^2\)
\(x^2 = 36 - 4\)
\(x^2 = 32\)

Step4: Take square root

\(x = \sqrt{32} \approx 5.656\) (or \(4\sqrt{2}\))

Answer:

\(x \approx 7.47\)

Question 9