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Activity C: Directions: Given right S XYZ with right angle at Y, find the missing part. 1. lfz= 10 and x = 24, find y. 2. ffz= 33 and x = 56, find y. 3. If y = 25 and x = 15, how long is z? 4. If x= 377 andz=213. find y, V Z Z 5. If y = 20 and x = 16, find z. X​

Activity C Directions Given Right S XYZ With Right Angle At Y Find The Missing Part 1 Lfz 10 And X 24 Find Y 2 Ffz 33 And X 56 Find Y 3 If Y 25 And X 15 How Lon class=

Sagot :

KAntoineDoixidn

✏️PYTHAGOREAN THEOREM

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[tex] \large \bold{\blue{DIRECTIONS:}} [/tex] Given right ∆XYZ with right angle at Y, find the missing part!

» Since ∆XYZ is a right triangle, we can solve its sides using the Pythagorean Theorem representing x and z as the legs and y as the hypotenuse.

[tex] \large \boxed{ \begin{align}& \sf y^2 = x^2 + z^2 \\ & \sf x^2 = y^2 - z^2 \\ & \sf z^2 = y^2 - x^2 \end{align}} [/tex]

[tex] \: [/tex]

#1: If z = 10 and x = 24, find y.

  • [tex] \sf y^2 = x^2 + z^2 [/tex]

  • [tex] \sf y^2 = 24^2 + 10^2 [/tex]

  • [tex] \sf y^2 = 576 + 100 [/tex]

  • [tex] \sf y^2 = 676 [/tex]

  • [tex] \sf \sqrt{y^2} = \sqrt{676} [/tex]

  • [tex] \sf y = 26 [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{y = 26 \: units}}} [/tex]

[tex] \: [/tex]

#2: If z = 33 and x = 56, find y.

  • [tex] \sf y^2 = x^2 + z^2 [/tex]

  • [tex] \sf y^2 = 56^2 + 33^2 [/tex]

  • [tex] \sf y^2 = 3136 + 1089 [/tex]

  • [tex] \sf y^2 = 4225 [/tex]

  • [tex] \sf \sqrt{y^2} = \sqrt{4225} [/tex]

  • [tex] \sf y = 65 [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{y = 65 \: units}}} [/tex]

[tex] \: [/tex]

#3: If y = 25 and x = 15, how long is z?

  • [tex] \sf z^2 = y^2 - x^2 [/tex]

  • [tex] \sf z^2 = 25^2 - 15^2 [/tex]

  • [tex] \sf z^2 = 625 - 225 [/tex]

  • [tex] \sf z^2 = 400 [/tex]

  • [tex] \sf \sqrt{z^2} = \sqrt{400} [/tex]

  • [tex] \sf z = 20 [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{z = 20 \: units}}} [/tex]

[tex] \: [/tex]

#4: If x = 3√2 and z = 2√3. find y.

  • [tex] \sf y^2 = x^2 + z^2 [/tex]

  • [tex] \sf y^2 = (3\sqrt2)^2 + (2\sqrt3)^2 [/tex]

  • [tex] \sf y^2 = 9(2) + 4(3) [/tex]

  • [tex] \sf y^2 = 18 + 12 [/tex]

  • [tex] \sf y^2 = 30 [/tex]

  • [tex] \sf \sqrt{y^2} = \sqrt{30} [/tex]

  • [tex] \sf y = \sqrt{30} [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{y = \sqrt{30} \: units}}} [/tex]

[tex] \: [/tex]

#5: If y = 20 and x = 16, find z.

  • [tex] \sf z^2 = y^2 - x^2 [/tex]

  • [tex] \sf z^2 = 20^2 - 16^2 [/tex]

  • [tex] \sf z^2 = 400 - 256 [/tex]

  • [tex] \sf z^2 = 144 [/tex]

  • [tex] \sf \sqrt{z^2} = \sqrt{144} [/tex]

  • [tex] \sf z = 12 [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{z = 12 \: units}}} [/tex]

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