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PLEASE!!!!!!Use the diagram and complete the steps to find the measure of the angle of depression from the top of the hoop to Lisa. The length of the shortest leg of the right triangle that is formed is __ feet. The angle of depression from the hoop to Lisa is ____ (congruent, complementary, supplementary) to the angle of elevation from Lisa’s line of sight to the hoop. Because the lengths of the opposite and adjacent sides are known, use the ___ (inverse sine, inverse cosine, inverse tangent) function. The angle of depression, rounded to the nearest degree, is approximately __(19, 21, 71) degrees.

PLEASEUse the diagram and complete the steps to find the measure of the angle of depression from the top of the hoop to Lisa The length of the shortest leg of t class=

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Answer:

Labelled the diagram as shown below.

From the given diagram:

Vertical distance from hoop to ground (AB) = 8.5 ft

BC=ED= 10 ft

BE = 5 ft

AE = AB-BE = 8.5 - 5 = 3.5 ft

First find the length of the shortest leg of the right triangle.

In a right  angle triangle AED.

ED = 10 ft

AE = 3.5 ft

Since, ED > AE

therefore, the length of the shortest leg of the right triangle that is formed is _3.5_ feet.

We know that:

The angle of depression is congruent to the angle of elevation as they form congruent angles on different parallel lines cut by a transversal line.

Therefore:

The angle of depression from the hoop to Lisa is __Congruent__ to the angle of elevation from Lisa’s line of sight to the hoop.

Use tangent ratio:

[tex]\tan \theta = \frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

In triangle AED

Opposite side = AE = 3.5 ft

Adjacent side = ED = 10 ft

then;

[tex]\tan \theta = \frac{3.5}{10} = 0.35[/tex]

where, [tex]\theta[/tex] is the angle of elevation.

⇒[tex]\theta = \tan^{-1} (0.35)[/tex] =19.2900462192 degree

The angle of elevation to the nearest degree is approximately, 19 degrees.

We know:

Angle of depression = Angle of elevation = 19 ft

⇒the angle of depression, rounded to the nearest degree, is approximately 19 ft.

Complete steps are shown below:

The length of the shortest leg of the right triangle that is formed is _3.5_ feet.

The angle of depression from the hoop to Lisa is __congruent__ (congruent, complementary, supplementary) to the angle of elevation from Lisa’s line of sight to the hoop.

Because the lengths of the opposite and adjacent sides are known, use the _inverse tangent_ (inverse sine, inverse cosine, inverse tangent) function. The angle of depression, rounded to the nearest degree, is approximately 19__(19, 21, 71) degrees.

Ver imagen OrethaWilkison

The angle made by the Lisa to the hoop is angle of elevation and angle made by hoop below the horizontal is angle of depression.

  • The length of the shortest leg of the right triangle that is formed is _3.5_ feet.
  • The angle of depression from the hoop to Lisa is __complementary__ to the angle of elevation from Lisa’s line of sight to the hoop.
  • Because the lengths of the opposite and adjacent sides are known, use the _inverse tangent__function.
  • The angle of depression, rounded to the nearest degree, is approximately _19_ degrees.

What is angle of depression and elevation?

The angle of depression is the angle, which is made between the horizontal line and the line of the observer vision below the line of imaginary horizontal line.

The angle of elevation is the angle, which is made between the horizontal line and the line of the observer vision above the line of imaginary horizontal line.

Given information-

The horizontal distance between the Lisa and basket is 10 ft.

The height of the basket from the ground is 8.5 ft.

The height of the horizontal sight of Lisa to the ground is 5 ft.

As the height of the basket from the ground is 8.5 ft and the height of the horizontal sight of Lisa to the ground is 5 ft. Thus the vertical height of the basket from the horizontal sight of Lisa is,

[tex]h=8.5-5\\h=3.5\rm ft[/tex]

This height is equal to the shortest leg of the right angle. Thus

The length of the shortest leg of the right triangle that is formed is 3.5 feet.

In the figure attached below the angle [tex]m\angle B[/tex] is 90 degrees.

The sum of all the angle of a triangle is equal to the 90 degrees. thus,

[tex]\angle A+\angle B+\angle C=180\\\angle A+90+\angle C=180\\\angle A+\angle C=180-90\\\angle A+\angle C=90^o[/tex]

As the sum of angle of hoop and angle of Lisa is equal to the 90 degrees.

Thus the angle of depression from the hoop to Lisa is complementary angle to the angle of elevation from Lisa’s line of sight to the hoop

The ratio of opposite side to the adjacent side is equal to the tangent of the angle for a right angle triangle as,

[tex]\rm tan\theta=\dfrac{opposite\; side}{adjacent\; side}\\\theta=\rm tan^{-1}\dfrac{opposite\; side}{adjacent\; side}\\[/tex]

Thus, the lengths of the opposite and adjacent sides are known, use the inverse tangent.

Put the values in the above formula as,

[tex]\theta=\rm tan^{-1}\dfrac{3.5}{10}\\\theta=19.29^o[/tex]

Thus, The angle of depression (rounded to the nearest degree) is approximately 19 degrees.

Hence,

  • The length of the shortest leg of the right triangle that is formed is _3.5_ feet.
  • The angle of depression from the hoop to Lisa is __complementary__ to the angle of elevation from Lisa’s line of sight to the hoop.
  • Because the lengths of the opposite and adjacent sides are known, use the _inverse tangent__ function.
  • The angle of depression, rounded to the nearest degree, is approximately _19_ degrees.

Learn more about the angle of depression here;

https://brainly.com/question/10217662

Ver imagen bhoopendrasisodiya34

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