# Precalculus : Trigonometric Applications

## Example Questions

### Example Question #1 : Area Of A Triangle

What is the area of a triangle with sides , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #9 : Area Of A Triangle

What is the area of a triangle with side lengths of , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #10 : Area Of A Triangle

What is the area of a triangle with side lengths , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #11 : Area Of A Triangle

What is the area of a triangle with side lengths , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #12 : Area Of A Triangle

What is the area of a triangle with side lengths , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #11 : Area Of A Triangle

What is the area of a triangle with side lengths , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #14 : Area Of A Triangle

What is the area of a triangle if the sides of a triangle are , and  ?

Explanation:

We can solve this question using Heron's Formula. Heron's Formula states that:

The semiperimeter is

where  are the sides of a triangle.

Then the area is

So if we plug in

So the area is

### Example Question #15 : Area Of A Triangle

The triangular fence of the T-rex in Jurassic park has sides a,b, and c measuring 100m, 110m, and 120m respectively. What is area of its enclosure?

Explanation:

Use Heron's formula to calculate the area:

A, B, and C are side lengths and s is calculated by:

.

Calculate s:

Plug side lengths and s into Heron's formula:

### Example Question #11 : Area Of A Triangle

Find the area of this triangle:

Explanation:

Use Heron's Formula

where

and

we can find  to be:

.

From here, plug in all our known values and solve.

### Example Question #17 : Area Of A Triangle

Find the area of this triangle:

Explanation:

To find the area, use Heron's Formula,

where

and

.

Here,

.

Now plug in all known values and solve.