Distance. Please help!?!?

Question

From the tope of a 100-m fire tower, a fire ranger observes two fires on opposite sides of the tower. The angle of depression to one fire is 5 degrees, and the angle of depression to the other fire is 6 degrees.

Assuming the base of the tower and the fires lie in the same horizontal line, what is the distance between the fires, correct to the nearest 100 m?

2000m
2100m
2200m
2300m

Thankyou

Answer 1

1000/cos5+1000/cos6=2000m

Answer 2

Set up the two triangles formed by the tower, the line from the top of the fire tower to each fire and the line from the base of the tower to each fire. The angle of depression and the angle of elevation are equal thus the angle formed at the corner where each fire is is equal to the angle of depression.

Each triangle is a right triangle where you know one angle, the opposite side, and you want to know the adjacent side.

This means that the distance from the base of the tower to one fire is 100/ tan (angle of depression).

thus length 1 = 100 / tan 5 and length 2 = 1/tan 6

length 1 = 1143m length 2 = 951m

total length = 2094m = 2100m

Answer 3

Think of two right triangles, back to back. The spine of the triangle is the 100 m tower. The angle from the top to the hypotenuse is 90-5, or 85 degrees on one side and 90-6, or 84 degrees on the other. You need to find the bases of the two triangles and add them together.

Let's start with the triangle with the 84 degree angle. A triangle has have three angles totaling 180 degrees. We have 84 + 90, the angle that the hypotenuse forms with the forest floor is 6 degrees.

By the law of sines, a/sin(a) = b/sin(b) = c/sin(c), so base/sin(84) = 100m/sin(6)

base = sin(84) * 100 m / sin(6) = 951.44 m

On the other side of the triangle, angle of depression is 5, so the interior angle is 90-5, or 85 degrees, so the base angle is 5, and we get

base = sin(85) * 100 m / sin(5) = 1143.00 m

Add the two and we get 951.44 m + 1143.00 m = 2094.44 m

Round up to 2100 m

Answer 4

Hi,

Angle of depression = angle of elevation from each fire so that the 100 meter tower is the opposite side of the triangle. Since tangent = opposite/adjacent, then:

tan 5 = 100/x and tan 6 = 100/z

Solving these for x and z,

x = 100/tan 5 and z = 100/tan 6
x = 100/.08749 and z = 100/.1051
x = 1143 and z = 951.4

1143 + 951.4 = 2094.4

To the nearest 100 m, that's 2100 m


I hope that helps!! :-)

Answer 5

I hate these math problems!!!