Question

Finf the exact value of sin A and cos A where a = 9 and b = 10 and <c is a right angle

Answer 1

to solve for the longest side, the hypotenuse, you have to use the pythagorean theorem. It will be 10^2 + 9^2 = c^2. 100 + 81 =c^2.
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)

Answer 2

sin A = 0.6666666667 ≈ 0.67

cos A = 0.7407407407 ≈ 0.74

Explanation:

The triangle above is a right angle triangle . Angle C is the angle 90°. we can use the cosine law for triangle to solve for side c.

c² = a² + b² - 2ab.cos(C)

a = 9

b = 10

C = 90°

c² = 9² + 10² - 2 × 9 × 10 cos( 90)

c² = 81 + 100 - 180 × 0

c² = 181

c = √181

c = 13.45362405 ≈ 13.5

Using sine rule

a/sin A = b/sin B = c/sin C

a = 9

b = 10

c = 13.5

C = 90°

9/sin A = 13.5/sin 90°

13.5 sin A = 9 × sin 90°

13.5 sin A = 9

sin A = 9/13.5

sin A = 0.6666666667

Use SOHCAHTOA principle to find cos A

cos A = b/c

cos A = 10/13.5

cos A = 0.7407407407