El angulo de depresion de un barco desde un acantilado es de 54° y si se acerca 150m a la costa es de 72° ¿cual es la altura del acantilado?

Step-by-step explanation:

the angle of depression of a boat from a cliff is 54 ° and if it approaches 150m to the coast it is 72 ° what is the height of the cliff?

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Using trigonometry on triangle ABC

tan x = opposite / adjacent

tan72 = h / 150

h = 150 × tan 72

h = 461.65 m

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Usando trigonometría en el triángulo ABC

tan x = opuesto / adyacente

tan72 = h / 150

h = 150 × tan 72

h = 461.65 m

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°