Question

The upper three fourths of a ship’s mast subtend at a point on the deck, an angle whose tangent is 0.75. If the whole mast subtends an angle  at the same point, then  is equal to

Answer 1

Step-by-step explanation:

Given The upper three fourths of a  ship's mast subtend at a  point on the deck, an angle  whose tangent is 0.75. If the  whole mast subtends an  angle o at the same point,  then tan is equal to​

Let OM be the mast height h and MN the upper three-fourth of it subtend an angle α at a point A on the deck.

Now angle MAN = α and tan α = 0.75

So let angle OAM = theta and OA = x

Now angle OAN = theta – α

So tan (theta – α) = ON / OA = h / 4x

So tan theta = h / x

  = 4 tan (theta – α)

So tan theta = 4(tan theta – tan α) / (1 + tan theta tan α)

So tan theta + tan^2 theta tan α = 4 tan theta – 4 tan α

So (3/4) tan ^2 theta – 3 tan theta + 4 (3/4) = 0

So tan^2 theta – 4 tan theta + 4 = 0

So (tan theta – 2)^2 = 0

Or tan theta = 2