In a right triangle with the hypotenuse c=10 and the acute angle A= 30 degrees 25' 30" find the sides a and b

a = 5.0 and b = 5.0

Step-by-step explanation:

Acute angle 30 degree 25' 30'' should be converted to degree as follows

30+25/60+30/3600.

30+0.4166+0.00833

30.425 degrees.

The acute angle A is facing a which means a is an opposite to it.

Using trig.

[email protected] = opposite/ hypotenuse

Sin 30.425 = a/10

a = 30.425 × 10

a = 5.0

For b.

[email protected] = adjacent/ hypotenuse

[email protected] = b/10

b = sin 30.425× 10

b = 5.0

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.