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 o at the same point,
then tane 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

Reference link will be

https://brainly.in/question/10023811