Answer:
a) The distance of the light's base from the bottom of the building is approximately: 5.2 ft
b) The length of the beam is approximately: 10.4 ft
Step-by-step explanation:
First, we have to recognize that we may draw a right triangle to picture our problem. Then, in order to find out the distance of the light's base from the bottom of the building, we need to use the tangent trigonometric function:
tan(angle) = opposite side / adjacent side
We know the angle and the opposite side and we want to find the adjacent side:
adjacent side = opposite side / tan(angle) = 9 ft / tan(60°) = 9 ft / = 9 ft / 1.73 = 5.2 ft
In order to find the length of the light beam, we use Pythagoras Theorem:
leg1²+leg2² = hyp²
Since the length of the beam corresponds to the hypotenuse and since we already know the length of the two legs, it is just a matter of substituting the values:
hyp = square_root(leg1²+leg2²) = square_root(9² + 5.2²) ft = square_root(108.4) ft = 10.4 ft
<span> The exponent is negative so we factor out -1:
</span>
Answer:
D. They have the same slope ( rate of change) and the same y-intercept.
Step-by-step explanation:
I y = 1.2x + 0.4.
II The slope is (10-4)/(8-3) = 6/5= 1.2.
Its equation is
y - 4 = (1.2)(x - 3)
y = 1.2x - 3.6 + 4
y = 1.2x + 0.4.
Answer:
<em>The perimeter is 72 units and the area is 149 square units.</em>
Step-by-step explanation:
has coordinates 
and 
Using the distance formula.........
Length of side 
Length of side 
Length of side 
So, the perimeter of the triangle will be: 
units. <em>(Rounded to the nearest unit)</em>
The height of the triangle for the corresponding base 
is 8.89 units.
<u>Formula for the Area of triangle</u>, 
So, the area of the will be: 
square units. <em>(Rounded to the nearest unit)</em>
9514 1404 393
Answer:
6.5 cm
Step-by-step explanation:
The Pythagorean theorem applies. You want c for a=1.6, b=6.3.
c² = a² +b²
c² = 1.6² +6.3² = 2.56 +36.69 = 42.25
c = √42.25 = 6.5
The length of the hypotenuse is 6.5 cm.
