## Rahaf 2 years ago A tree standing vertically on level ground casts a 140 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 24.7°. Find the height of the tree to the nearest foot.

1. cwrw238

|dw:1366148873008:dw|

2. cwrw238

you use trigonometry to solve this x is height of the tree which trigonometric ratio do we use here?

3. cwrw238

the trig ratios are sine, cosine and tangent - do u know what each of those are?

4. Rahaf

I'm really not good at this i tried many times

5. cwrw238

they are the ratios of the different sides in a right angled triangle |dw:1366149664499:dw|

6. cwrw238

x is the angle O = opposite side H = hypotenuse (longest side) A = adjacent side sin x = O / H cos x = A / H tan x = O / A

7. cwrw238

you remember these by memorizing the following bit of nonsense SOH-CAH-TOA

8. cwrw238

in a right angled traingle you can find lengths of sides and angles as long you know the value of another 2 sides/angles

9. cwrw238

in your problem you know one angles 24.7 degrees and you know the adjacent side 140 and you need to find the opposite side x = 24.7, A = 140 and O = ? so you have O and A (TOA) so u need to use the tangent (T) tan 27.4 = x / 140 so x = 140* tan 24.7 grab your calculator and you can work this out

10. cwrw238

hope this helps sorry but I gotta go right now

11. Rahaf

Got it, thank you so much :)