The base of a right angled triangle is one third
of its altitude. If its hpotenuse is root 40 cm then the altitude is
Answers
Step-by-step explanation:
Hint: We apply trigonometry height and distance formula. In which we use either tanθ, sinθ or cosθ opposite to θ is your perpendicular other is base. This kind of question is used to find the height and distance of things these are for.
Formula used:
Tanθ=PerpendicularBase
Complete step-by-step answer:
Lighthouse = 80 meters (Given)
Let the distance of ship 1 from the base of the lighthouse = x meters and let the distance between 2 ships = y meters.
Also given that the angle of depression of two ships on the same side of the light house in horizontal line with its base is 40∘&30∘ respectively.
AB=80 m(Height of lighthouse)BC=distance of ship 1 from light house baseBD=distance of ship 2 from lighthouse base
In △ABCtanθ=PerpendicularBase⇒Tanθ=ABBCby putting the values of θ=40∘ AB=80 BC=x⇒Tan40=80x⇒⋅8391=80xBC=80⋅8391⇒x=95⋅34
In △ABD Tanθ=PerpendicularBaseputting the values θ 30∘ AB=80, BD=x+y⇒Tan30=ABBD⇒13–√⇒AB x+y
⇒x+y=3–√ AB (Cross Multiplication)95⋅34+y=1⋅73×80 (Substitute Values)
⇒95⋅34+y=138⋅56⇒ y=138.56−95⋅34⇒ y=43⋅22m(approximately)
∴Distance between two ships=CD=y=43⋅22m
43m as answer in nearest metre .
Additional information:
To find the height of a hill, tower, star etc. We can use this formula. This formula is applicable for right angled triangles.
Note: We apply tanθ= perpendicular/ base in this we use value of tan40∘=⋅8391 and we use this formula in two triangles △ ABC and △ ABD and simplifying find the value of x and y. Please do mention the units as required in the question as in this question they mentioned that find the answer to the nearest metre
