Question

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:

Answer 1

The equation that can be used to find the height of the tree is as follows:

$\frac{h}{sin 29} =\frac{40}{sin147}$

The height of the tree is 35.6 m

How to use sine rule to find height of the tree?

Th equation that can be used to find the height of the tree uses the principle of sine rule.

Therefore,

$\frac{h}{sin 29} =\frac{40}{sin(180-4-29)}$

$\frac{h}{sin 29} =\frac{40}{sin147}$

Therefore,

$\frac{h}{sin 29} =\frac{40}{sin147}$

cross multiply

h sin 147 = 40 sin 29°

h = 40 sin 29° / sin 147

h = 19.3923848099 / 0.54463903501

h = 35.6015636045

h = 35.6 m

learn more on sine rule here: brainly.com/question/15221233

#SPJ1