What is side e

Angle d and angle f
Please let me know asap

9514 1404 393

e ≈ 9.608D ≈ 46.5°F ≈ 38.5°

Step-by-step explanation:

The only given angle is between the two given sides, so the Law of Cosines must be used to find the side opposite the angle. It tells you ...

  e² = d²+f² -2df·cos(E)

  e² = 7² +6² -2·7·6·cos(95°) ≈ 92.321082

  e ≈ 9.608

The remaining angles can be found from the law of sines.

  sin(D)/d = sin(E)/e

  D = arcsin(d/e·sin(E)) ≈ arcsin(7/9.608·sin(95°)) ≈ 46.5°

  F = 180° -95° -46.5° = 38.5°

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.