Trigonometry help and show work please

Question

The angle of elevation from a boat to the top of a cliff is 33. A sign is directly at the top of the cliff. The angle of elevation from the boat to the top of the sign is 37. If the sign is 40ft high, how far is the boat from the cliff. (The sign sits atop the cliff. So, the top of the cliff to the top of the sign is 40ft).

Answer 1

Draw and label a diagram

d is the distance from the hill to the boar

h is the height of the hill

h / d = tan 33°

h = d tan 33°

(h + 40) / d = tan 37°

h + 40 = d tan 37°

h = d tan 37° - 40

d tan 33° = d tan 37° - 40

d tan 33° - d tan 37° = -40

d (tan 33° - tan 37°) = -40

d = -40 / (tan 33° - tan 37°)