Question

If in triangle ABC angle B=90° and sin A=7/25 then, find the cosA and cosC.

Answer 1

Answer:

cosA = 24/25, cosC = 7/25

Step-by-step explanation:

In triangle ABC,

sinA = 7/25 = p/h

For Angle A,

let p = 7k and h = 25k

As we know that by Pythogoras theorem,

h² = p² + b²

or,b² = h² - p²

or,b² = (25k)² - (7k)²

or,b² = 625 k² - 49 k²

or,b² = 576k²

Therefore,b = 24k

cosA = b/h

or,cosA = 24k/25k

or,cosA = 24/25

For Angle C,

h = 25k

p = 24k

b = 7k

Now,

cosC = b/h

or,cosC = 7k/25k

or,cosC = 7/25

NOTE :-

Thus , sinA = cos C because A & C are complementary Angles

since A + B + C = 180⁰

& given B = 90⁰

Therefore, A + C = 90⁰

C = 90⁰ - A

Now as we know,

$\sin(θ) = \cos(90° - θ)$

sin A = cos (90⁰ - A)

or, sin A = cos C

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Answer 2

cos A=24/25,cos C=7/25

Step-by-step explanation:

sin A =7/25

BC =7,AC=25

IN TRIANGLE ABC ,

ACC TO PGT (PHYTHAGORAS THEORM )

AB²+BC²=AC²

(AB²)+(7)²=(25)²

AB²+49=625

AB²=625-49

AB²=576

AB= SQUARE ROOT (576)

AB=2×2×2×2×2×2×3×3

WE TAKE ONE COMMON FROM EVERY PAIR

AB=2×2×2×3

AB=24

NOW,

COS A =AB/AC

I.E. 24/25

AND ,

COS C=BC/AC

I.E. 7/25

I HOPE U WILL UNDERSTAND