Question

Challenge Problem

Answer 1

Answer: his distance from the pole is 90.16 ft

Explanation:

based on the diagram of the question i will upload along this answer;

45 - d is equal to part of the pole below the horizontal line

d/x = tan(16) ; x = d/tan(16)............equ1

(45-d) / x = tan(12); x = (45-d) / tan(12)-----------equ2

∴ d/tan(16) = (45-d) / tan(12)

d.tan(12) = (45-d).tan(16)  

d.tan12 = (45×tan16) - d.tan16

0.2125d = 12.9034 - 0.2867d

0.2125d + 0.2867d = 12.9034

0.4992d = 12.9034

d = 12.9034/0.4992

d = 25.85 ft

now substitute value of d into any of our previous equation, lets take equation 1

x = 25.85 / tan(16)

x = 25.85 / 0.2867

x = 90.16 ft

Therefore his distance from the pole is 90.16 ft