How do I solve for any of the variables, with explanation if you can please? Thank you

Question

asked Oct 25, 2024 154k views

1 Answer

Spyros · Answer 1 · 2024-10-30T10:00:48+0000

Answer:

a = 18.6 ft ; b = 16.7 ft ; ∠B = 42° ; ∠C = 90°

Explanation:

c = 25 ft

∠C = 90°

∠A = 48°

Using angle sum property of triangle, we can find ∠B.

∠B = 180 - 48 - 90

= 180 - 138

= 42°

We can find a and b using trigonometry ratio Sin and Cos.

$\sf Sin \ A = (opposite \ side \ of \ \angle A )/(hypotenuse)\\\\ Sin \ 48 = (a)/(c)\\\\ 0.7431 =(a)/(25)\\\\\\$

0.7431*25 = a

$\boxed{\bf a = 18.6 \ ft }$

To find the value of b, use Cosine ratio,

$\sf Cos \ A = (adjacent \ side \ of \ \angle A)/(hypotnuse)\\\\ Cos \ 48 = (b)/(25)\\\\\\0.6691= (b)/(25)$

0.6691 * 25 = b

$\boxed{b = 16.7 \ ft}$