Question

PLs help

1. A) Given the provided angle and the leg provided, what trigonometric ratio is used to find the hypotenuse? Write out the equation using the ratio and angle.

B) What is the length of EG rounded to the nearest hundredth? Include units.

C) What is the measure, in degrees, of angle E?

D) What is length of EF rounded to the nearest hundredth? Include units.

E) What is the area of triangle EFG? Include units.



2.A regular hexagon has an edge length of 4 cm. What is the exact area of the hexagon? Do not answer with a decimal.

Hint: Draw a picture, draw & find the length of the apothem, use the formula for area of regular polygons to find the area. Include correct units.


3. A. The center of a circle is (-3, 7) with a radius is 11. Write out the standard equation of the circle:

B. The center of a circle is (1, -2) with a radius is 2. Draw the circle below.

4. Part A) 1 point, name of what kind of conic section is this: x - 2 = ½ (y+ 4)²





Part B) 2 points, what is the vertex of this parabola? y - 3 = ½ (x + 5)²





Part C) 2 points, what is the center of this circle? x² + y² = 81


5. What shape results from a cross-section that is parallel to plane BCDA?

6. A sandbox is in the shape of a rectangular prism with dimensions 48 in.× 60 in. ×12 in.


The sandbox is 75% filled with sand. A new delivery of sand, the shape of a cube with a side length of 19 in., is dumped in the sandbox. How many cubic inches of space remain in the sandbox after the delivery? Include proper units in your final answer.

Picture 1 below goes with question 1

Picture 2 below goes with question 3

Picture 3 below goes with question 5

Thx for the help

Answer 1

A) The hypotenuse is the longest side of the triangle .In the figure EG is the hypotenuse.The given angle is <G=40 degrees.The side adjacent is FG= 10 units.

The question is asking us to find the trigonometry ratio which will help us find EG.We can use cos as cos is ratio of adjacent and hypotenuse.

`cos 40=(10)/(Hypotenuse EG.)`

B) Cos 40 =0.766.

Substituting tan40 value we have:

`0.766=(10)/(EG)`

EG=13.05.

C)Sum of angles in triangle is 180.

<E+<F+<G=180

<E+90+40=180

<E+130=180

<E=50 degrees.

D)
`Tan  40=(EF)/(10)`

EF=8.39

E) Area of triangle EFG=
`(1)/(2)x base x height.`

A rea of the triangle =
`(1)/(2)x8.39x13.05`

Area= 54.75 square units.