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Solve the triangle. Round decimal answer to the nearest tenth...

Solve The Triangle Round Decimal Answer To The Nearest Tenth class=

Sagot :

Maggielee724idn

Answer:

DE ≈ 16.1, ∠E ≈ 60.3°, ∠D ≈ 29.7°

Step-by-step explanation:

use pythagorean theorem:

DE² = 8² + 14² => DE = √8² + 14² ≈ 16.1

use inverse tangent function:

∠E =  [tex]tan^{-1}[/tex](14/8) ≈ 60.3°

∠D =  [tex]tan^{-1}[/tex](8/14) ≈ 29.7°

View image Maggielee724
View image Maggielee724

Answers:

  • side DE = 16.1 units
  • angle E = 60.3 degrees
  • angle D = 29.7 degrees

The "units" and "degrees" portions of the answers are likely to be left out.

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Explanation:

Since we have a right triangle, we can use the pythagorean theorem to find the hypotenuse DE

a^2+b^2 = c^2

c = sqrt(a^2+b^2)

c = sqrt(8^2+14^2)

c = 16.124515496597

c = 16.1 is the approximate length of side DE

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We'll use the tangent ratio to find angle E

tan(angle) = opposite/adjacent

tan(E) = FD/FE

tan(E) = 14/8

E = arctan(14/8)

E = 60.2551187030578

E = 60.3 degrees

The notation arctan is the same as inverse tangent. You should have a [tex]\tan^{-1}[/tex] button on your calculator to help compute the inverse tangent.

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We could use the tangent ratio to solve for angle D, by noting that

tan(D) = 8/14

or we could use the idea that D+E = 90 which solves to D = 90-E

D = 90-E

D = 90-60.3

D = 29.7 degrees

Note how arctan(8/14) = 29.74488 which rounds to 29.7

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