﻿ Sine, Cosine, Tangent Real World Applications. How to use SOHCAHTOA to calculate the height of trees, buildings etc..
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# Sine, Cosine, Tangent Applications

The Sine, Cosine and Tangent functions are often applied to real world scenarios.

##### Example 1

What is the height of the tree below?

$tan(16) = \frac{opp}{adj} \\ tan(16) = \frac{14}{\red x} \\ \red x = \frac{14}{tan(16)} \\ \red x = 48.8$

##### problem 1

$tan(55) = \frac{opp}{adj} \\ tan(55)= \frac{\red x }{ 57} \\ \red x = 57 \cdot tan(55) \\ \red x = 81.4$

##### Problem 2
Step 1

First, you should draw and label a picture of this word problem.

Step 2

The illustration:

Rest of Steps

Now, set up your trig ratio and solve for a side length:

##### Problem 3
Step 1

First, you should draw and label a picture of this word problem.

Step 2

The illustration:

Rest of Steps

Now, set up the tangent ratio and solve for a side length:

##### Problem 4
Step 1

First, you should draw and label a picture of this word problem.

Step 2

The illustration:

Rest of Steps

Now, set up your trig ratio and solve for a side length: