Find the height of a tree with angles 17˚ and 15˚. The angles are seperated by 31.4 feet.?

Question

Find the height of a tree with angles 17˚ and 15˚. The angles are seperated by 31.4 feet.

Tree
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|_____17˚_| 31.4 ft |___15˚

Answer 1

First get the adjacent angle of 17˚
180˚ - 17˚ = 163˚

Then get the third angle of the triangle formed by the vertex of the 15˚-angle, vertex of 163˚ angle and the top of tree.
180˚ - 15˚ - 163˚ = 2˚

Then get the length from the vertex of the 15˚-angle to the top of the tree using sine law.
31.4 / sin 2˚ = x / sin 163˚
x = 31.4*sin 163˚ / sin 2˚
x = 263.1 ft

Finally get the height of the tree (h) using sine (or any trigonometric identities taking into account the angle to be used.
sine 15˚ = h / 263.1
h = 263.1 * sin 15˚
h = 68.1 ft

So the height of the tree is approximately 68.1 ft.

Answer 2

68.1 is your tree height.

You MIGHT want to look at the right triangle(s) taking the 2 acute angles at the top of the tree (73 deg, and 75 deg)

tan 73 = x / h where x is the distance from tree base to vertex of 17 deg angle, and h = tree height

tan 75 = (x+31.4) / h

Eliminate x from the 2 equations; solve for h.

(FWIW x = 222.7 feet; so x + 31.4 = 254.1)

Answer 3

Let the height of the tree be h and the distance from the base to the farther most point (where angle is 15) be x ...
Tan 15 = h / x .... x = h / Tan 15

Tan 17 = h / (x-31.4) ........x-31.4 = h /Tan 17 ............. x = h/Tan 17 + 31.4

So h/Tan 15 = (h/Tan 17) + 31.4
h/Tan 15 - h/Tan 17 = 31.4
h = 31.4 (Tan 15)(Tan 17) / (Tan 17 - Tan 15)

Substitute Tan 15 and Tan 17 values to get h, the height of the tree.

Answer 4

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Answer 5

Let

h= height of tree
x = horizontal distance to tree from 17° angle
x + 31.4 = horizontal distance to tree from 15° angle

tan = opposite side / adjacent side

tan 17° = h / x
tan 15° = h / (x + 31.4)

x = h / tan 17°
x + 31.4 = h / tan 15°
x = h / tan 15° - 31.4

h / tan 17° = h / tan 15° - 31.4
h / tan 17° - h / tan 15° = -31.4
h / tan 15° - h / tan 17° = +31.4
h * tan 17° - h * tan 15° = 31.4(tan 15°)(tan 17°)
h(tan 17° - tan 15°) = 31.4(tan 15°)(tan 17°)
h = 31.4(tan 15°)(tan 17°)/(tan 17° - tan 15°)
h = 68.1 feet

Answer 6

let a and b be the length from the leg of tree to the point of each angle
h is the height of the tree
a + 31.4 = b
we have : tan 17 / tan15 = b / a <=> a * tan17 = b*tan15 = (a + 31.4)*tan15
=> a =31.4 / (tan17 - tan15) = 831 ft
h = a * tan17 = 254 ft

Answer 7

let the heightbe h andthe horizontal dist be x
h=xtan15*
h=(x+31.4)tan 17*
solve for x
substitute toget h

Answer 8

831'-1 1/8" or 68'-1"