# From point 135 feet from the base of a tree, the angle from ground level to the top of the tree is 49* (degrees), how do you find the height of the tree?

Apr 3, 2018

The height of the tree is $\text{155.3 feet}$.

#### Explanation:

This involves trigonometric ratios. A key concept of remembering how to do this is learning soh-cah-toa. Strange right?

It helps to find sine, cosine, and tangent. For

• $\text{Sin"= "opposite"/"hypotenuse}$
• $\text{Cos" = "adjacent"/"hypotenuse}$
• $\text{Tan" = "opposite"/"adjacent}$

It helps to draw out a picture . Ignore the poor drawing skills. Anyways, you can see it forms a right triangle.

When it labeled, you see we'll be using tangent, which is opposite over adjacent to find $x$ (the height of the tree). Set up a proportion.

$T a n \frac{49}{1} = \frac{x}{135}$

Cross-mulitiply and you get

$x = 135 \times T a n \left(49\right)$

Plug that into the calculator and you get $155.299734974836$. Rounded to the nearest tenth, it is $\text{155.3 feet}$.