Question

Lenny is planning to cut down a pine tree. He has parked his truck 90 feet away from the base of the tree and wants to make sure that the tree will not hit his truck when it falls. The angle of elevation from the base of the truck to the top of the tree is 50°. How tall is the tree to the nearest foot? Should Lenny move his truck?
A)
58 feet; no
B)
69 feet; no
C)
75 feet; no
D)
107 feet; yes

Answer 1

Well, if the elevation is 45 degrees, the height of the tree and the distance to the truck are the same.

The elevation is more than that, so the distance to the truck is less than the height of the tree. 

The only answer that reflects that is D.

Answer 2

Answer:

D)  107 feet; yes

Step-by-step explanation:

Given :

Lenny has parked his truck 90 feet away from the base of the tree.

The angle of elevation from the base of the truck to the top of the tree is 50°

To Find: How tall is the tree to the nearest foot?

Solution :

Refer the attached figure

Since we are given that truck is 90 feet away from tree i.e. BC = 90 feet

The angle of elevation from the base of the truck to the top of the tree is 50° i.e. ∠ACB = 50°

Now to calculate the height of tree i.e. AB

Using trigonometric ratios :

$\frac{Perpendicular}{Base} = Tan \Theta$

$\frac{AB}{BC} =Tan 50^{\circ}$

$\frac{AB}{90} =1.19175359$

$AB =1.19175359*90$

$AB =107.2578231$

Thus AB = 107.2578231≈107 feet

Hence , The height of tree is 107 feet

Yes, Lenny should move his truck .

Option D is correct.