Question

Asked 4 times, please help

Answer 1

3.0 miles

Explanation:

Let h be the height

Tan(27) = h/b

h = btan(27)

Tan(45) = h/(9-b)

(9-b)tan(45) = h

(9-b)tan(45) = btan(27)

9tan(45) = b[tan(45) + tan(27)]

b = 5.962138633

h = btan(27) = 3.037861367

Answer 2

Denote the two points are A and B, the balloon is C. Then we have,

Side AB = 9 miles

Angle CAB (angle A) = 27 deg

Ange CBA (angle B) = 45 deg

=> Angle ACB (angle C) = 180 - 27 - 45 = 108 deg

Applying the sine theorem:

AB/sinC = BC/sinA

=> BC = AB x sinA/sinC = 9 x sin27/sin108 = 4.3 miles

Denote CH as the height from C to side AB (or distance from ground to balloon), we have:

CH = BC x sin B = 4.3 x sin*45 = ~3.04 miles

=> Distance from ground to balloon: ~3.04 miles

Hope this helps!

:)