The latest academics question and answer inquired students to express what they feel is the most important element for a student to do in order for you to achieve success. The one which response stood out from the rest was practice. Persons who are always successful do not become successful by being born. They work hard and dedication their lives to succeeding. If you wish to fulfill your goals, keep this in mind! down below are one of the answer and question example that you will possibly utilise to practice and improve your practical knowledge and also give you insights that might assist you to preserve your study in school.

## Question:

caleb and emily are standing 100 yards from each other. caleb looks up at a 45 degree angle to see a hot air balloon. Emily looks yup at a 60 degree angle to see the same hot air ballon. approximate how far is the hot air ballon off the ground?

## Answer:

The **height **of the air balloon is** 63.4 yards**.

**What is a trignometry?**

**Trigonometry **is a branch of mathematics that uses variables to determine heights and distances. It is the study of the properties of right angled **triangles **and **trigonometric **functions and of their applications.

For the given situation,

The diagram below shows the situation described above.

The distance between Caleb and Emily = 100 yards

Let the distance from Caleb to the air balloon be ‘x’

Let the distance from Emily to the air balloon be ‘y’

Let height of the air balloon be ‘h’

⇒

⇒

We know that, θ =

Now consider the **triangle **with angle 45°,

° =

We know that tan 45° = 1 and substitute x = 100-y,

⇒

⇒

This is equation 1.

Now consider the **triangle **with angle 60°,

° =

We know that, tan 60° = √3

⇒

⇒

This is the equation 2.

On equating equation 1 and 2,

⇒

⇒

⇒

⇒

Thus height,

Substitute the value of y in h,

⇒

⇒

⇒

⇒

⇒

Hence we can conclude that the **height **of the air balloon is** 63.4 yards**.

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