# Trigonometry : Trigonometric Applications

## Example Questions

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### Example Question #1 : Triangles

In right triangle , where  and , what is ?

This triangle cannot exist.

Explanation:

This triangle can exist. Since  is a right angle, we can use the Pythagorean Theorem, where  is the hypoteneuse:

### Example Question #2 : Triangles

Given a right triangle where , find the missing side.

Explanation:

Since the triangle in question is a right triangle we can use the Pythagorean Theorem. First, we must determine which sides we are given. Since the function we are given is sine, we know that we are given the opposite side and the hypotenuse. Therefore, setting up the equation:

Where,  and  are given.

Solving the above equation:

We toss out the negative solution since the length of a side must be positive.

### Example Question #3 : Triangles

Given a right triangle where , find the missing side.

Explanation:

Since the triangle in question is a right triangle we can use the Pythagorean Theorem. First, we must determine which sides we are give. Since the function we are given is tangent, we know that we are given the opposite and adjacent sides. Therefore, setting up the equation:

Where,  and  are given.

Solving the above equation:

We toss out the negative solution since the length of a side must be positive.

### Example Question #4 : Triangles

Given a right triangle where , find the missing side.

Explanation:

Since the triangle in question is a right triangle we can use the Pythagorean Theorem. First, we must determine which sides we are given. Since the function we are given is cosine, we know that we are given the adjacent side and hypotenuse. Therefore, setting up the equation:

Where,  and  are given.

Solving the above equation:

We toss out the negative solution since the length of a side must be positive.

### Example Question #5 : Triangles

Given the accompanying triangle where  and , determine the length of the hypotenuse.

Explanation:

We are given the opposite side, with respect to the angle, along with the angle. Therefore, we utilize the sine function to determine the length of the hypotenuse:

Substituting the given values:

Cross multiplying:

Solving for :

### Example Question #6 : Triangles

Given the accompanying right triangle where  and , determine the measure of  to the nearest degree.

Explanation:

We are given two sides of the right triangle, namely the hypotenuse and the opposite side of the angle. Therefore, we simply use the sine function to determine the angle:

In order to isolate the angle we must apply the inverse sine function to both sides:

### Example Question #7 : Trigonometric Applications

All the squares are equal, and there are 6 squares in the figure.

What is the value of   ?

Explanation:

### Example Question #7 : Triangles

While waiting for your sister to finish her bungee jump, you decide to figure out how tall the platform she is jumping off is. You are standing  feet from the base of the platform, and the angle of elevation from your position to the top of the platform is  degrees. How many feet tall is the platform?

Explanation:

You can draw the following right triangle using the information given by the question:

Since you want to find the height of the platform, you will need to use tangent.

Make sure to round to  places after the decimal.

### Example Question #8 : Triangles

When the angle of elevation of the sun is  degrees, a flagpole casts a shadow that is  feet long. In feet, how tall is the flagpole?

Explanation:

You can draw the following right triangle from the information given by the question.

In order to find the height of the flagpole, you will need to use tangent.

Make sure to round to  places after the decimal.

The flagpole is  feet tall.

### Example Question #9 : Triangles

A ladder that is  feet long is resting against the side of a house at an angle of  degrees. In feet, how far up the side of the house does the ladder reach?