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

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 =  (14/8) ≈ 60.3°

∠D =  (8/14) ≈ 29.7°

Answers:

side DE = 16.1 unitsangle E = 60.3 degreesangle 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 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

The correct answer is -4

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.