MATH SOLVE

8 months ago

Q:
# 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.

Accepted Solution

A:

Answer:Labelled the diagram as shown below.From the given diagram:Vertical distance from hoop to ground (AB) = 8.5 ftBC=ED= 10 ftBE = 5 ftAE = AB-BE = 8.5 - 5 = 3.5 ftFirst find the length of the shortest leg of the right triangle.In a right angle triangle AED.ED = 10 ftAE = 3.5 ftSince, ED > AEtherefore, 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 AEDOpposite side = AE = 3.5 ftAdjacent side = ED = 10 ftthen;[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 degreeThe 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.