Question

if sec theata =25/7 then find the value of tan theata

Answer 1

Hey!

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sec ϴ = Hypotenuse / Base

Given,

sec ϴ = 25/ 7

Then,
Hypotenuse = 25
Base = 7
Perpendicular = ?

Using Pythagoras theorem,

H² = P² + B²
25² = P² + 7²
625 = P² + 49
625 - 49 = P²
√576 = P
P = 24

We know,
tanϴ = Perpendicular / Base
tanϴ = 24 / 7

Thus,
tanϴ = 24 / 7
Option (D) is correct.

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Hope it helps!

Answer 2

We know that secant for any angle in a right angled triangle is equal to the ratio of its hypotenuse to its base.
Hence,
sec A = h / b


I will be assuming (theta) to be ( A ).

Now,
sec A = 25 / 7 [ According to the question ]

Simply substituting what we just found at the beginning,
h / b = 25 / 7

Let, h = 25x and b = 7x
By Pythagoras Theorem,
h² = p² + b²
( 25x )² = p² + ( 7x )²
=> 625x² = p² + 49x²
=> p² = 625x² - 49x²
=> p² = 576x²
=> p = √576x²
=> p = 24x

Now, we know that,
tan A = p / b
tan A = 24x / 7x
Hence, tan A = 24/7

Therefore, the correct answer is option D.