Question

question 4 (1 point)
right triangle with legs 4 and 8, hypotenuse x
x=
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question 5 (1 point)
right triangle with legs 7 and 10, hypotenuse x
x=
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question 6 (1 point)

Explanation:

Question 4

Step1: Identify triangle type (right triangle)

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 4\), \(b = 8\), and \(c = x\) (hypotenuse).

Step2: Apply Pythagorean theorem

Substitute values: \(4^2 + 8^2 = x^2\)
Calculate: \(16 + 64 = x^2\)
Simplify: \(80 = x^2\)
Take square root: \(x = \sqrt{80} = 4\sqrt{5} \approx 8.94\) (or exact form \(4\sqrt{5}\))

Step1: Identify triangle type (right triangle)

Right triangle, use Pythagorean theorem: \(a^2 + b^2 = c^2\), with \(a = 7\), \(b = 10\), \(c = x\) (hypotenuse).

Step2: Apply Pythagorean theorem

Substitute: \(7^2 + 10^2 = x^2\)
Calculate: \(49 + 100 = x^2\)
Simplify: \(149 = x^2\)
Take square root: \(x = \sqrt{149} \approx 12.21\) (or exact form \(\sqrt{149}\))

Answer:

\(4\sqrt{5}\) (or approximately \(8.94\))

Question 5