Answer :
The angle of elevation of the ground is 30.5°
Step-by-step explanation:
Height of the tree=10 foot
length of the shadow=17 foot
we have to determine the angle of elevation of the ground
The tree, shadow and ground forms a right triangle with tree as the height, shadow as the base.
The angle of elevation of the ground θ
tanθ=opposite/adjacent
[tex]=tree length/shadow length\\=10/17\\\\=0.588\\[/tex]
θ[tex]=tan^-1(0.588)=30.5 \°[/tex]
The angle of elevation of the ground is 30.5°
The angle of the elevation of the ground is 30.5 degrees and it can be determined by using trigonometric ratios.
Given that,
A 10-foot tree casts a 17-foot shadow directly down a slope when the angle of elevation of the sun is 42 degrees.
We have to determine
The angle of elevation of the ground.
According to the question,
The height of the tree is 10-foot,
And the height of the shadow is 17-foot.
The angle of the elevation of the ground is given by the following formula,
[tex]\rm Tan\theta = \dfrac{Length \ of \ the \ tree}{Length \ of \ man\ shadow}[/tex]
Substitute all the values in the formula,
[tex]\rm Tan\theta = \dfrac{Length \ of \ the \ tree}{Length \ of \ man\ shadow}\\\\Tan\theta = \dfrac{10}{17}\\\\Tan\theta = 0.17\\\\\theta = tan{-1}(0.17)\\\\\theta = 30.5 \ degree[/tex]
Hence, The angle of the elevation of the ground is 30.5 degrees.
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