Question

During the summer fire season, a fire is spotted from two forest service fire towers. Let's call them tower A and tower B.......tower A estimates that they are 45 miles from the fire and tower B estimates that they are 60 miles from the fire. If the angle where the fire is located measures 62°, how far apart are the two fire towers? Round to the nearest tenth of a mile.

Answer 1

Explanation:

Two fire towers and the spot of fire make a triangle . The two sides of the triangle are 45 miles and 60 miles and they are inclined at an angle of 62° . If a and b are two sides and C is the angle between them . c is the side opposite to angle C then

From trigonometric formula

cos C =
`(a^2+b^2-c^2)/(2ab)`

Putting the given values

cos62 =
`(45^2+60^2-c^2)/(2* 45* 60)`

2535.15 = 2025 + 3600 - c²

c² = 3089 . 85

c = 55.58 miles.