Respuesta :
Answer:
3.97°
Step-by-step explanation:
Let
θ = desired angle
α =32° - θ = the angle above ground to the top of the slope
θ = 32° - a
If angle of the sun is 32° above a level horizon, then the angle at the top of the slope is given as δ = 90 - 32 = 58°. Now we can measure a
38/sin(58°) = 21/sin a
sin a = [21 sin(58°)]/38
Sin a = 0.47
a = arcsin 0.47 = 28.03
Since,
θ = 32° - a
θ = 32° - 28.03° = 3.97°
The required angle of elevation of the ground is θ =3.97°
Given that,
A 21-foot tree casts a 38-foot shadow directly down a slope,
When the angle of elevation of the sun is 32 degrees.
We have to determine,
Find theta, the angle of elevation of the ground .
According to the question,
Let , The angle θ = desired angle
And α =32° - θ = the angle above ground to the top of the slope
θ = 32° - a
The angle of the sun is 32° above a level horizon,
Then, the angle at the top of the slope is given as δ = 90 - 32 = 58°.
Therefore, to measure the angle a is given by,
[tex]\dfrac{38}{sin58} = \dfrac{21}{sina} \\\\Sina = \dfrac{21 \times sin58}{38}\\\\Sina = 0.47\\\\a = sin^{-1} (0.47)\\\\a = 28.03[/tex]
Therefore, The value of θ is,
[tex]\theta = 32 - a\\\\\theta = 32-28.03\\\\\theta = 3.97[/tex]
Hence, The required angle of elevation of the ground is θ = 3.97°.
To know more about Trigonometry click the link given below.
https://brainly.com/question/15315742
