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?

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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?

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Answer 1 · 2018-04-03T02:07:08

The height of the tree is $155.3 feet$ $"155.3 feet"$ .

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

$sin = \frac{opposite}{hypotenuse}$ $"Sin"= "opposite"/"hypotenuse"$

$cos = \frac{adjacent}{hypotenuse}$ $"Cos" = "adjacent"/"hypotenuse"$

$tan = \frac{opposite}{adjacent}$ $"Tan" = "opposite"/"adjacent"$

It helps to draw out a picture . enter image source here 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 $x$ $x$ (the height of the tree). Set up a proportion.

$\frac{tan (49)}{1} = \frac{x}{135}$ $Tan(49)/ 1 = x/135$

Cross-mulitiply and you get

$x = 135 \times tan (49)$ $x = 135 times Tan(49)$

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

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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?

1 Answer

Explanation:

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