Math

posted by .

Two dogs are 180 ft apart on opposite sides of a tree. The angles of elevation from the dogs to the top of the tree are 35 degrees and 23 degrees.

What is the height of the tree?

• Math -

Let X be the distance of the dog with the 35 degree elevation angle from the tree. The other dog is 180-X away (in feet). Let H be the height of the tree. You have these two equations in two unknowns:
H/X = tan 35 = 0.7002075
H/(180-X) = tan 23 = 0.4244748
Solve for X first by eliminating H.
(180-X)/X = tan35/tan23 = 1.64959
180 - X = 1.64959 X
X = 180/2.64959 = 67.935 feet
180-X = 112.065 ft
H = X tan 35 = 47.569 ft

• Math -

Thanks!

Similar Questions

1. math [basic trig]

Sam and Markus are standing on level ground 100m apart. A large tree is due North of Markus and on a bearing of 065degrees from Sam. The top of the tree appears at an angle of elevation of 25 degrees to Sam and 15 degrees to Markus. …
2. trig

Because of prevailing winds, a tree grew so that it was leaning 4 degrees from the vertical. At a point, 35 meters from the tree, the angle of elevation to the top of the tree is 23 degrees. Find the height h of the tree
3. physics

if im standing 28 meters from a tree....the tree is leaning 7 degrees vertically away from u...the degree of elevation is 26 degrees from feet to tree...whats the height of the tree?
4. geometry

a tree grew at a 3 degree slant from the vertical. at a point 60 feet from the tree, the angle of elevation to the top of the tree is 14 degrees. find the height of the tree to the nearest tenth of a foot.
5. maths --plse help me..

THERE IS A SMALL ISLAND IN THE MIDDLE OF A 100M WIDE RIVER AND A TALL TREE STANDS ON THE ISLAND.pAND q RE POINTS DIRECTLY OPPOSITE EACH OTHER ON THE TWO BANKS AND IN LINE WITH THE TREE.IF THE ANGLE OF ELEVATION OF THE TOP OF THE TREE …
6. CST GEOMETRY

a tree is situated on level ground from a point 135 feet from the base of the tree the measure of the angle of elevation from the ground to the top of the tree is 43 degrees which is the height of the tree to the nearest foot?
7. Math

1. A rangers tower is located 44m from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 28 degrees and the angle of depression to the base is 36 degrees. How tall is the tree?
8. Precalc/Trig

I have no idea how to solve this one problem: Round to two decimal places. Two observers 25 feet apart, sight to the top of the tree. If the angle of elevation to the top of the tree from the observer closest to the tree is 30 degrees …
9. geometry

At a point on the ground 50 feet from the front of a tree, the angle of elevation to the top of the tree is 48 degrees. Find the height of the tree.
10. Math , trigonometry

From a point on the ground 20m from the base of a tree the angle of the elevation to the top of the tree is 47 degrees. Calculate the height the of the tree correct to the nearest metre ?

More Similar Questions