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

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 :

Thus AB = 107.2578231≈107 feet

Hence , The height of tree is 107 feet

Yes, Lenny should move his truck .

Option D is correct.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

a. 12.5 kg

step-by-step explanation:

f = ma

so

m = f/a = (2500 n)/(200 m/s²) = 12.5 kg

1 n = 1 kg·m/s²