## capooza 3 years ago a civil engineer needs to measure the length of a proposed tunnel through a mountain. the engineer chooses a point that can be seen from each end of the tunnel and measures the distances to each end of the proposed tunnel to be 3,000 and 4,200 meters respectively. if the angle between the two distances is 113 degrees, what is the length of the tunnel to the nearest meter?

1. UnkleRhaukus

|dw:1323664183040:dw|

2. UnkleRhaukus

$x^2 = a^2 + b^2 - 2ab cos( \theta )$

3. UnkleRhaukus

$(xkm)^2=(3km)^2+(4.2km)^2-2\times (3km) \times (4.2km) \times cos (113°)$

4. capooza

ok, i've gotten that far, but when i tried to go any further, i got a weird square root of a negative. and i'm pretty sure that's not possible.

5. UnkleRhaukus

$(xkm)^2= 26.64km^2-25.2km^2 \times 0.99527$$=26.64km^2-25.08km^2$$= 1.559km^2$$xkm = 1.2487km$$xm=1249m$ ...the tunnel is 1249 meters long

6. capooza

i had to turn that quiz in, so i have no idea if that's what i got, but thanks anyway!