Question

as observed from the top of 75m high Lighthouse from the sea-level, the angles of depression of two ships are 30 and 45 degree. if one ship is exactly behind the other on the same side of lighthouse, find the distance between the two ships

Answer 1

i think it will help you

Answer 2

$\large\tt\red{In\:∆ABC,}$

$\longrightarrow$$\large\tt\purple{tan\:45°=\frac{AB}{BC}}$

$\longrightarrow$$\large\tt\purple{\frac{75}{BC}=1}$

$\therefore$$\longrightarrow$$\large\tt\purple{BC=75m}$

$\large\tt\red{In\:∆ABD,}$

$\longrightarrow$$\large\tt\purple{tan\:30=\frac{AB}{BD}}$

$\longrightarrow$$\large\tt\purple{\frac{1}{√3}=\frac{75}{BC+CD}}$

$\longrightarrow$$\large\tt\purple{\frac{1}{√3}=\frac{75}{75+CD}}$

$\longrightarrow$$\large\tt\purple{75√3=75+CD}$

$\longrightarrow$$\large\tt\purple{75(√3-1)m=CD}$

$\therefore$$\small\tt\underline\blue{The\:distance\:between\:the\:two\:ships\:is\:75(√3-1)m}$