Respuesta :
Let the height of the three be h and the distance between student A and the tree be x, then
tan 57 = h/x
x = h/tan 57
tan 46 = h/(x + 1)
x + 1 = h/tan 46
h/tan 57 + 1 = h / tan 46
h / tan 46 - h / tan 57 = 1
h(tan 57 - tan 46) = tan 46 tan 57
h = tan 46 tan 57 / (tan 57 - tan 46) = 3.2 yards
tan 57 = h/x
x = h/tan 57
tan 46 = h/(x + 1)
x + 1 = h/tan 46
h/tan 57 + 1 = h / tan 46
h / tan 46 - h / tan 57 = 1
h(tan 57 - tan 46) = tan 46 tan 57
h = tan 46 tan 57 / (tan 57 - tan 46) = 3.2 yards
Using the Law of sines to solve the problem, we can say that the height of the tree is 3.159 yards.
What are the height and distance?
It is the application of trigonometry. Trigonometry deals with the sides and angles of the triangle.
Given
Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.
To find
The height of the tree.
Let the height of the tree be h.
Let the distance between the tree and student B be x.
Let the distance between the tree and student A be y.
The distance between student A and student B is 1 yard.
Then the relation between student A, student B, and Tree will be.
1 + y = x Then
In ΔBTC
[tex]\begin{aligned} \rm tan\ \theta &= \rm \dfrac{perpendicular}{base} \\\rm tan 46 &= \dfrac{h}{x} \\h &= 1.035*x\\\end{aligned}[/tex]...1
In ΔATC
[tex]\begin{aligned} \rm tan\ \theta &= \dfrac{perpendicular}{base} \\\rm tan 57 &= \dfrac{h}{x-1} \\h &= 1.539*(x-1)\\\end{aligned}[/tex]...2
From equations 1 and 2
[tex]\begin{aligned} 1.537*(x-1) &= 1.035*x\\\\(1.539-1.035)x &= 1.539\\\\x &= \dfrac{1.539}{0.504} \\\\x &= 3.053\\\end{aligned}[/tex]
Then from equation 1, the height of the tree will be
h = 1.035 x 3.053h = 3.159 yards.
Thus, the height of the tree is 3.159 yards.
More about height and distance link is given below.
https://brainly.com/question/10681300
