Question

A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground. What is the height x, to the nearest foot, of the balloon? A) 85 feet B) 96 feet C) 115 feet D) 128 feet

I know the setup is like this,
Sin(50) =(x/150)
(but I don't have a calculator and the online ones aren't working - plz help)

Answer 1

115 feet

Explanation:

Given : A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground.

To Find: What is the height x, to the nearest foot, of the balloon?

Solution:

We are given a set up :

`sin 50 ^(\circ)=(x)/(150)`

Using scientific calculator find the value of sin 50

0.76604

`0.76604=(x)/(150)`

`0.76604 * 150=x`

`114.906=x`

Hence the height of the balloon is 115 feet.

Option C is correct.

Answer 2

C) 115 feet

Explanation:

Assuming your setup is correct and the question is asking the height, given that the length of the slant rope is 150 ft, you find x by multiplying the equation by 150:

... 150*sin(50°) = x ≈ 115 ft

Almost any on-line calculator will compute this value. If you don't specifiy the angle is degrees, you will need to verify that it is properly interpreted. (It may be interpreted as radians. Different calculators make different assumptions.)

The Google or Bing search boxes are pretty reliable calculators. Usually * is suitable as the multiplication indicator, and / works for division. They follow the order of operations rigorously, so parentheses are needed for numerators, denominators, and exponents when more than a single number is involved.

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There are on-line equation solvers, too. I've found them to be more fussy and less useful. One likes to give irrational results as the ratio of two (large) integers, for example.