Answer all of them need this

the longer base of an isosceles trapezoid measures 22 ft. the nonparallel sides measure 8 ft, and the base angles measure 75°. find the length of a diagonal.

a. 17 ft
b. 21 ft
c. 20 ft
d. 25 ft

a triangular field has sides of 218.5 m and 224.5 m, and the angle between them measures 58.20 . find the area of the field.
a. 41,690 m²
b. 12,924 m²
c. 14,332 m²
d. 20,845 m²

First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in , we can easily find the values of CQ and BQ.

Since,

ft

In a similar manner we can find BQ as:

ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

Let us now consider

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of .

feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area=(First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

Area=

Therefore, Option D is the correct option.

Third Question

For this question we will apply the Sine Rule to the given to us.

Thus, from the triangle we will have:

This gives to be:

Which is not close to any of the given options.

Fourth Question

Please find the second attachment for a better understanding of the solution provided her.

As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.

miles.

Thus, Option D is the answer.