can someone help and explain how to do this?

You’re work is a bit cluttered so I can’t tell what applies to this problem but I think you’re overthinking the question a bit. Let’s note that we have one leg of the right triangle and the hypotenuse. Since we have both angles, we can choose whether we want to use sine or cosine. I’m going to choose sine. We know that sin(θ) = opposite/hypotenuse. Thus, we can fill in values and get sin(30 deg) = x/5. We can then solve for x and simplify since sin(30 deg) is on the unit circle

x = 5 sin(30 deg) = 5 (1/2) = 5/2
Your answer x = 5 sin (30) / sin(90) is correct, you just need to take the last step of plugging in what sin(30) and sin(90) are.  Using law of sines is not the usual way to solve this problem but its not incorrect. (Law of Sines applies to ANY TRIANGLE and is typically used when the triangle is NOT a right triangle and its the only method that will work. Since this IS a right triangle you can just consider sine or cosine directly as the other commenter demonstrated)

You should know the values for sine, cosine, tangent of the basic angles like 0, 30, 45, 60, 90 degrees. Those are ones that teachers traditionally expect you to memorize.
You might notice that you can make an equilateral triangle by mirroring the triangle on the base. Then it is trivial that x is just 5/2
You know that formula a = c * sin(phi), in this very question you are asked to find a. C = 5 and calculating the sin is quite a thorny one.

Lets write sin as an infinite series: sin(a) = sum over n = 0 to inf of (-1)^n * x^(2n+1) / (2n+1)! Where ! is a factorial

The factorial of n is a product of the terms k where k is over a range from 1 to n

Then let's prove that this series is convergent

lim abs( (-1) ^n / (2n+1)! / (-1) ^n+1 / (2n+3)!) = 0 then this series is convergent then we can find a sum

Sum of (-1) ^n * (a) ^2n+1 / (2n+1)! Where a = pi/6

Sum of (-1) ^n * (pi/6) ^2n+1 / (2n+1)! This sum converges to sin(pi/6) = 1/2

Hence a = 5/2
Are we not able to use the relationship of special right triangles? 30-60-90

0 like 0 dislike